- title: 'Distilling Safe LLM Systems via Soft Prompts for On Device Settings' abstract: 'Deploying safe large language models ({LLMs}) on resource-constrained edge devices presents a critical challenge: while dual-model systems combining {LLMs} with guard models provide effective safety guarantees, their substantial memory and computational demands make them prohibitively expensive for on-device deployment. This paper presents a comprehensive study of parameter-efficient safety alignment methods for resource-constrained settings. Through systematic evaluation across multiple {LLM} architectures, training objectives, and parameter-efficient fine-tuning approaches, we identify that \textbf{soft prompts combined with distillation-based training consistently outperform alternative methods}. We introduce distillation frameworks based on total variation and KL divergence that effectively transfer safety behaviors from guard models into learned soft prompts. Our evaluations on various benchmarks demonstrate that this combination achieves superior safety-usefulness trade-offs compared to {LoRA} adapters, steering vectors, and direct optimization methods, while requiring minimal additional memory and compute at inference time. These findings establish soft prompt distillation as the preferred approach for safety alignment in on-device {LLM} deployment.' volume: 337 URL: https://proceedings.mlr.press/v337/alfarra26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/alfarra26a/alfarra26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-alfarra26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Motasem family: Alfarra - given: Cristina family: Pinneri - given: Dana family: Kianfar - given: Mohammed family: Almousa - given: Christos family: Louizos editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1-18 id: alfarra26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1 lastpage: 18 published: 2026-08-06 00:00:00 +0000 - title: 'Contrastive Conformal Sets' abstract: 'Contrastive learning produces coherent semantic feature embeddings by encouraging positive samples to cluster closely while separating negative samples. However, existing contrastive learning methods lack a principled construction of geometric sets in the semantic feature space with distribution-free guarantees at any user-specified coverage level. We extend conformal prediction to this setting by introducing covering sets equipped with learnable generalized hyper-ball constraints. We propose a method that constructs conformal sets guaranteeing user-specified coverage of positive samples while maximizing negative sample exclusion. We theoretically motivate volume minimization as a proxy for negative exclusion, enabling our approach to operate effectively even when negative pairs are unavailable. The positive inclusion guarantee inherits the distribution-free coverage property of conformal prediction, while negative exclusion is maximized through learned set geometry optimized on a held-out training split. Experiments on simulated and real-world image datasets demonstrate improved inclusion-exclusion trade-offs compared to standard distance-based conformal baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/alkhatib26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/alkhatib26a/alkhatib26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-alkhatib26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yahya family: Alkhatib - given: Wee Peng family: Tay editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 19-38 id: alkhatib26a issued: date-parts: - 2026 - 8 - 6 firstpage: 19 lastpage: 38 published: 2026-08-06 00:00:00 +0000 - title: 'PCU: Perturbation-Calibrated Uncertainty for Unsupervised Anomaly Detection' abstract: 'Unsupervised anomaly detection requires deciding whether a test observation belongs to the nominal data distribution when only normal data are available for training. In this setting, failures arise primarily from epistemic uncertainty: the model must determine whether a sample lies within the learned support of the data or in an unseen region of the input space. Existing methods rely on density surrogates, reconstruction error, or distance-based scores, which often become unreliable near the nominal manifold and do not explicitly encode uncertainty. We propose \emph{Perturbation-Calibrated Uncertainty ({PCU})}, a representation-learning framework that estimates epistemic uncertainty through controlled input perturbations. An encoder is trained on a ladder of known corruption magnitudes so that latent displacement varies predictably with perturbation strength, enforced by a ranked-sensitivity constraint, a scale-aware prediction head, and variance–covariance regularization. An exponential moving average of clean embeddings provides a reference, yielding an anomaly score that combines global displacement, learned perturbation sensitivity, and local stability. By making perturbation response an intrinsic property of the representation rather than a post hoc test, {PCU} provides a compact, label-free uncertainty signal for unsupervised anomaly detection. Experiments on diverse tabular benchmarks demonstrate stable anomaly scores and competitive detection performance, particularly in near-manifold regimes, while mixed-feature perturbation design remains a limitation of the current {Gaussian} instantiation. {PCU} source code is available on \href{https://github.com/M-Allaoui/{PCU}.git}{{GitHub}}.' volume: 337 URL: https://proceedings.mlr.press/v337/allaoui26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/allaoui26a/allaoui26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-allaoui26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mebarka family: Allaoui - given: Rachid family: Hedjam - given: Mohand Saïd family: Allili - given: Guoqiang family: Zhong editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 39-61 id: allaoui26a issued: date-parts: - 2026 - 8 - 6 firstpage: 39 lastpage: 61 published: 2026-08-06 00:00:00 +0000 - title: 'Curvature-Weighted Capacity Allocation: A Minimum Description Length Framework for Layer-Adaptive Large Language Model Optimization' abstract: 'Layer-wise capacity in large language models is highly non-uniform: some layers contribute disproportionately to loss reduction, whereas others are nearly redundant. Existing layer-scoring methods provide sensitivity estimates but do not give a principled rule for converting those estimates into allocation or pruning decisions under a global hardware budget. We introduce a curvature-aware, MDL-inspired framework built around the layer gain $\zeta_k^2=g_k^\top\widetilde H_{kk}^{-1}g_k$. This quantity equals twice the maximal decrease predicted by the regularized layer-restricted quadratic model and incorporates inverse local curvature; it is therefore a local surrogate for reducible risk, not a universal dominance claim over gradient-norm scores. After normalizing the gains into scores $q_k$, we formulate two convex programs: one allocates expert slots under diminishing returns, and the other assigns layer-wise pruning ratios while protecting high-score layers. Both continuous programs have unique globally optimal solutions characterized by one dual variable and computable in $O(K\log(1/\varepsilon))$ time by bisection. We also prove a quadratic transfer-regret bound: when source and target score vectors differ by at most $\delta$, the target surrogate cost of the transferred decision is within $O(\delta^2)$ of the target optimum. Experiments on {Mistral-7B} and Gemma-7B show clear allocation gains in some settings and competitive, though mixed, pruning performance. The framework therefore replaces an empirical score-to-decision heuristic with a budget-feasible optimization procedure whose guarantees apply to the stated continuous surrogates. Code is available on github repo - \href{https://github.com/TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation.git}{TKAI-LAB-Mali/Curvature-Weighted-Capacity-Allocation}' volume: 337 URL: https://proceedings.mlr.press/v337/amaefuna26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/amaefuna26a/amaefuna26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-amaefuna26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Theophilus family: Amaefuna - given: Hitesh Ulhas family: Vaidya - given: Anshuman family: Chhabra - given: Ankur family: Mali editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 62-86 id: amaefuna26a issued: date-parts: - 2026 - 8 - 6 firstpage: 62 lastpage: 86 published: 2026-08-06 00:00:00 +0000 - title: 'When and How Often is Weighted Majority Vote Optimal Under Log Loss?' abstract: 'Modern machine learning methods often require large, high quality labeled datasets, whose labels are potentially expensive and time consuming to obtain. One solution, seen in Programmatic Weak Supervision, crowdsourcing, and semi-supervised learning, is to cheaply obtain an ensemble of noisy labeling functions (LFs) and combine their predictions. Specifically, weighted majority vote ({WMV}) is a simple but well studied method to perform such a combination. Weighting strategies for {WMV} can be derived from a wide ranging set of assumptions (e.g. probabilistic, adversarial, etc.). However, existing analyses often suppose that the LF predictions are fixed, and characterize the conditions when said weighting strategies are optimal (among all weighting strategies). We take a different approach and show that all weighting strategies which only depend on LF accuracies, e.g. majority vote, are optimal (w.r.t. log loss) on a measure zero set of problems. A method to compute the proportion of problems where such aforementioned strategies are $\epsilon$ close to being optimal is presented and run. Other contributions include improved analysis of {WMV}’s excess error under log loss.' volume: 337 URL: https://proceedings.mlr.press/v337/an26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/an26a/an26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-an26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Steven family: An - given: Sanjoy family: Dasgupta editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 87-132 id: an26a issued: date-parts: - 2026 - 8 - 6 firstpage: 87 lastpage: 132 published: 2026-08-06 00:00:00 +0000 - title: 'Workload-Preserving Differentially Private Synthetic Data for Causal Inference via Maximum-Entropy Calibration' abstract: 'Workload-based differentially private ({DP}) synthetic data methods privately measure aggregate queries and post-process the noisy answers into synthetic records. Generic workloads can achieve strong distributional fidelity, but causal estimands such as the average treatment effect ({ATE}) depend on treatment-arm balance and outcome moments that generic marginals need not preserve. We propose causal workloads: {DP} query sets designed around the orthogonal moments used by doubly robust causal estimators. The released workload can be used directly by stable moment-map estimators or reconstructed by maximum-entropy calibration into reusable synthetic data; our theory decomposes {ATE} error into sampling, privacy, workload-approximation, Monte Carlo, and calibration terms. We also introduce Causal-AIM, an adaptive workload selector, and a noise-aware multiple-imputation (NA+MI) procedure for confidence intervals from {DP} synthetic data. Because the workload is released once, the same {DP} synthetic table can support {ATE}, {ATT}, and subgroup analyses without additional privacy spending. Empirically, causal workloads are most useful at strict privacy budgets and for calibrated uncertainty, while generic workloads often retain an advantage for point RMSE as privacy relaxes. The broader lesson is a tradeoff: distributional fidelity can help point accuracy, but valid causal inference requires preserving causal moments and propagating {DP} noise rather than treating synthetic rows as real.' volume: 337 URL: https://proceedings.mlr.press/v337/asiaee26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/asiaee26a/asiaee26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-asiaee26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Amir family: Asiaee - given: Kaveh family: Aryan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 133-160 id: asiaee26a issued: date-parts: - 2026 - 8 - 6 firstpage: 133 lastpage: 160 published: 2026-08-06 00:00:00 +0000 - title: 'Partial Causal Structure Learning for Valid Selective Conformal Inference under Interventions' abstract: 'Selective conformal prediction can yield substantially tighter uncertainty sets when we can identify calibration examples that are exchangeable with the test example. In interventional settings, such as perturbation experiments in genomics, exchangeability often holds only within subsets of interventions that leave a target variable "unaffected" (e.g., non-descendants of an intervened node in a causal graph). We study the practical regime where this invariance structure is unknown and must be estimated from data. Our main result quantifies how coverage degrades when the estimated safe calibration set accidentally includes interventions that affect the target, and gives a conservative correction when an upper bound on this error is available. Rather than learning a full causal graph, we learn only the intervention-target relationships needed to choose calibration interventions. We give algorithms for this partial learning task and evaluate them on synthetic structural equation models and {Replogle} {K562} {CRISPR}-interference data, where the experiments illustrate synthetic gains from selective calibration and finite-sample tradeoffs on real perturbation screens.' volume: 337 URL: https://proceedings.mlr.press/v337/asiaee26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/asiaee26b/asiaee26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-asiaee26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Amir family: Asiaee - given: Kaveh family: Aryan - given: James P. family: Long editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 161-184 id: asiaee26b issued: date-parts: - 2026 - 8 - 6 firstpage: 161 lastpage: 184 published: 2026-08-06 00:00:00 +0000 - title: 'Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment' abstract: 'Randomized controlled trials (RCTs) are the gold standard for estimating treatment effects, yet they are often underpowered for detecting effect heterogeneity. Large observational studies (OS) can supplement RCTs for conditional average treatment effect (CATE) estimation, but a key barrier is covariate mismatch: the two sources measure different, only partially overlapping, covariates. We propose {CALM} (Calibrated ALignment under covariate Mismatch), which learns embeddings that map each source’s features into a common representation space. OS outcome models are transferred to the {RCT} embedding space and calibrated using trial data, preserving causal identification from randomization. Finite-sample risk bounds decompose into alignment error, outcome-model complexity, and calibration complexity terms, making explicit when the learned embedding is accurate enough to reduce variance. We instantiate {CALM} in two forms: a closed-form linear version, {CALM-Lin}, and a neural representation-learning version, {CALM-NN}. Across 51 simulation settings, calibration-based linear methods are effectively tied in linear-CATE regimes, while {CALM-NN} wins all 22 nonlinear-CATE settings by wide margins. Moreover, on two real-data studies {CALM-NN} delivers the largest gains over the trial-only baseline.' volume: 337 URL: https://proceedings.mlr.press/v337/asiaee26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/asiaee26c/asiaee26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-asiaee26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Amir family: Asiaee - given: Samhita family: Pal editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 185-209 id: asiaee26c issued: date-parts: - 2026 - 8 - 6 firstpage: 185 lastpage: 209 published: 2026-08-06 00:00:00 +0000 - title: 'Certified Interventional Fidelity: Anytime-Valid, Adaptive Evaluation of Causal Claims in Mechanistic Interpretability' abstract: 'Mechanistic interpretability often evaluates explanations by intervening on a model: swapping hidden states, patching activations, ablating components, or comparing a compressed model to the original one. These experiments are usually summarized by a point estimate, even though the evaluation may be monitored while it runs or adapted toward suspected failures. This makes it hard to tell whether a reported fidelity or patching effect is a stable causal claim or a consequence of finite sampling and evaluation choices. We introduce Certified Interventional Fidelity ({CIF}), a statistical layer for interventional interpretability evaluations. {CIF} first writes the quantity being reported as a causal estimand: an expectation of a bounded score over a stated input distribution and a stated intervention distribution. It then provides confidence intervals and anytime-valid confidence sequences for this estimand, including under adaptive intervention sampling via bounded mixture importance weighting. We instantiate {CIF} with {Hoeffding}-style sequences and variance-adaptive betting sequences, the latter reducing certification cost by $10$–$30\times$ in our experiments. On {MNIST} abstractions and {GPT-2} Small {IOI} circuits, {CIF} certifies high-fidelity claims, shows when apparent method differences are not statistically supported, and makes sensitivity to the intervention distribution explicit.' volume: 337 URL: https://proceedings.mlr.press/v337/asiaee26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/asiaee26d/asiaee26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-asiaee26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Amir family: Asiaee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 210-227 id: asiaee26d issued: date-parts: - 2026 - 8 - 6 firstpage: 210 lastpage: 227 published: 2026-08-06 00:00:00 +0000 - title: 'Probably Correct Optimal Stable Matching under Two-Sided Uncertainty' abstract: 'We study a sequential learning problem for stable matchings in two-sided markets where preferences on both sides are initially unknown. We focus on a centralized setting where an algorithm matches agents at each time step and receives noisy rewards that reflect the preferences of the matched agents, following a semi-bandit feedback structure. We adopt a pure exploration perspective, aiming to efficiently identify the optimal stable matching with high probability. Our work extends prior results by handling \emph{two-sided uncertainty} and by exploiting \emph{partial preference} information. A central ingredient is the notion of \textbf{pervasive stable matching}, which enables the identification of optimal stable matchings under partial preferences. We propose elimination-based algorithms whose stopping criteria exploit the structure of the learned partial preferences, and provide a refined sample-complexity analysis. Beyond pure exploration, we extend our approach to regret minimization and establish regret bounds with respect to the \emph{optimal} stable matching that avoid dependence on the minimum reward gap $\Delta_{\min}$.' volume: 337 URL: https://proceedings.mlr.press/v337/athanasopoulos26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/athanasopoulos26a/athanasopoulos26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-athanasopoulos26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Andreas family: Athanasopoulos - given: Anne-Marie family: George - given: Christos family: Dimitrakakis editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 228-254 id: athanasopoulos26a issued: date-parts: - 2026 - 8 - 6 firstpage: 228 lastpage: 254 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Transfer Learning With Side Information' abstract: 'Robust {Markov} Decision Processes ({MDPs}) address environmental shift through distributionally robust optimization (DRO) by finding an optimal worst-case policy within an uncertainty set of transition kernels. However, standard DRO approaches require enlarging the uncertainty set under large shifts, which leads to overly conservative and pessimistic policies. In this paper, we propose a framework for transfer under environment shift that derives a robust target-domain policy via $\textit{estimate-centered}$ uncertainty sets, constructed through constrained estimation that integrates limited target samples with side information about the source-target dynamics. The side information includes bounds on feature moments, distributional distances, and density ratios, yielding improved kernel estimates and tighter uncertainty sets. Error bounds and convergence results are established for both robust and non-robust value functions. Moreover, we provide a finite-sample guarantee on the learned robust policy and analyze the robust sub-optimality gap. Under mild low-dimensional structure on the transition model, the side information reduces this gap and improves sample efficiency. We assess the performance of our approach across OpenAI Gym environments and classic control problems, consistently demonstrating superior target-domain performance over state-of-the-art robust and non-robust baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/awad26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/awad26a/awad26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-awad26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Akram family: Awad - given: Shihab family: Ahmed - given: Yue family: Wang - given: George K. family: Atia editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 255-286 id: awad26a issued: date-parts: - 2026 - 8 - 6 firstpage: 255 lastpage: 286 published: 2026-08-06 00:00:00 +0000 - title: 'Gaussian Process Limit Reveals Structural Benefits of Graph Transformers' abstract: 'Graph transformers are the state-of-the-art for learning from graph-structured data and are empirically known to avoid several pitfalls of message-passing architectures. However, there is limited theoretical analysis on why these models perform well in practice. In this work, we prove that attention-based architectures have structural benefits over graph convolutional networks in the context of node-level prediction tasks. Specifically, we study the neural network gaussian process limits of graph transformers (GAT, {Graphormer}, Specformer) with infinite width and infinite heads, and derive the node-level and edge-level kernels across the layers. Our results characterise how the node features and the graph structure propagate through the graph attention layers. As a specific example, we prove that graph transformers structurally preserve community information and maintain discriminative node representations even in deep layers, thereby preventing oversmoothing. We provide empirical evidence on synthetic and real-world graphs that validate our theoretical insights, such as integrating informative priors and positional encoding can improve performance of deep graph transformers.' volume: 337 URL: https://proceedings.mlr.press/v337/ayday26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ayday26a/ayday26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ayday26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nil family: Ayday - given: Lingchu family: Yang - given: Debarghya family: Ghoshdastidar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 287-327 id: ayday26a issued: date-parts: - 2026 - 8 - 6 firstpage: 287 lastpage: 327 published: 2026-08-06 00:00:00 +0000 - title: 'Dynamic Regret in Outlier-Oblivious Online Optimization using Nonconvex Robust Losses' abstract: 'We study a robust online convex optimization framework, where an adversary can introduce outliers by corrupting loss functions in an arbitrary number of rounds $k$, unknown to the learner. In contrast to prior works, we consider both bounded and unbounded domains and allow for large gradients for the losses without relying on a Lipschitz assumption or any prior knowledge of $k$. We introduce the Log Exponential Adjusted Robust and iNvex ({LEARN}) loss, a non-convex (invex) robust loss function to mitigate the effects of outliers and develop a robust variant of the online gradient descent algorithm by leveraging the {LEARN} loss. We establish dynamic regret guarantees with respect to the uncorrupted rounds and conduct experiments to validate our theory. Our upper bound matches the existing lower bound in the bounded domains and is tight (up to logarithmic factors) in the unbounded domains. Furthermore, we present a unified analysis framework for developing online optimization algorithms for non-convex (invex) losses, utilizing it to provide regret bounds with respect to the {LEARN} loss, which may be of independent interest.' volume: 337 URL: https://proceedings.mlr.press/v337/barik26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/barik26a/barik26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-barik26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Adarsh family: Barik - given: Anand family: Krishna - given: Vincent Y. F. family: Tan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 328-363 id: barik26a issued: date-parts: - 2026 - 8 - 6 firstpage: 328 lastpage: 363 published: 2026-08-06 00:00:00 +0000 - title: 'Stop Probing, Start Coding: Why Linear Probes and Sparse Autoencoders Fail at Compositional Generalization' abstract: 'Foundational to interpreting pretrained representations of deep generative models, the linear representation hypothesis states that neural network activations encode high-level concepts as linear mixtures. However, linear representation does not imply linear accessibility of such concepts: under superposition, when the number of concepts exceeds the activation dimension, recovering the underlying latent factors requires sparse nonlinear inference, making methods such as linear probes insufficient. Sparse autoencoders ({SAEs}) perform nonlinear inference but amortize it into a fixed encoder, introducing a systematic amortization gap. We show this gap dominates all other error sources and persists as the number of training samples is increased, causing {SAEs} to fail under out-of-distribution ({OOD}) compositional shifts. In contrast, classical sparse coding with per-sample iterative inference leverages compressed sensing guarantees to recover latent factors robustly, maintaining near-zero gaps in the accuracy between in and out of distribution. Our results demonstrate that the recent {OOD} failures of {SAEs} can be attributed to amortization failures: per-sample inference at test time substantially improves {OOD} performance, even when using a dictionary learned by an {SAE}. This is observed along a spectrum of hybrid approaches that progressively undo amortization and recover {OOD} performance.' volume: 337 URL: https://proceedings.mlr.press/v337/barin-pacela26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/barin-pacela26a/barin-pacela26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-barin-pacela26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Vitória family: Barin-Pacela - given: Shruti family: Joshi - given: Isabela family: Camacho - given: Simon family: Lacoste-Julien - given: David family: Klindt editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 364-412 id: barin-pacela26a issued: date-parts: - 2026 - 8 - 6 firstpage: 364 lastpage: 412 published: 2026-08-06 00:00:00 +0000 - title: 'Gradual Uncertainty Refinement via Noise-Driven Curriculum: A Post-Hoc Meta-Model for Robust Uncertainty Quantification' abstract: 'Reliable uncertainty quantification remains a major obstacle to the deployment of deep learning models under distributional shift. Existing post-hoc approaches that retrofit pretrained models either inherit misplaced confidence or merely reshape predictions, without advising the model when to be uncertain. We introduce {GUIDE}, a lightweight evidential learning meta-model that attaches to a frozen deep learning model and is explicitly guided on when and how to be uncertain. {GUIDE} identifies salient internal features via a calibration stage and then uses these features to construct a noise-driven curriculum that teaches the model when and how to express uncertainty. {GUIDE} requires no retraining, no architectural modifications, and no manual intermediate-layer selection to the base deep learning model, thus ensuring broad applicability and minimal user intervention. The resulting model avoids distilling overconfidence from the base model, improves out-of-distribution detection ($\approx$ 77%) and adversarial attack detection ($\approx$ 80%), while preserving in-distribution performance. Across diverse benchmarks, {GUIDE} consistently outperforms state-of-the-art approaches, evidencing the need for actively guiding uncertainty to close the gap between predictive confidence and reliability.' volume: 337 URL: https://proceedings.mlr.press/v337/barker26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/barker26a/barker26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-barker26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Charmaine family: Barker - given: Daniel family: Bethell - given: Simos family: Gerasimou editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 413-447 id: barker26a issued: date-parts: - 2026 - 8 - 6 firstpage: 413 lastpage: 447 published: 2026-08-06 00:00:00 +0000 - title: 'Anomaly detection in time-series via inductive biases in the latent space of conditional normalizing flows' abstract: 'Deep generative models for anomaly detection in multivariate time-series are typically trained by maximizing observed data likelihood. However, likelihood in observation space measures marginal density rather than conformity to structured temporal dynamics, and therefore can assign high probability to anomalous or out-of-distribution samples. We address this structural limitation by relocating the notion of anomaly to a prescribed latent space. We introduce explicit inductive biases in conditional normalizing flows, modeling time-series observations within a discrete-time state-space framework that constrains latent representations to evolve according to prescribed temporal dynamics. Under this formulation, expected behavior corresponds to compliance with a specified distribution over latent trajectories, while anomalies are defined as violations of these dynamics. Anomaly detection is consequently reformulated as a statistically grounded compliance test, such that observations are mapped to latent space and evaluated via goodness-of-fit tests against the prescribed latent evolution. This yields a principled decision rule that remains effective even in regions of high observation likelihood. Experiments on synthetic and real-world time-series demonstrate reliable detection of anomalies in frequency, amplitude, and observation noise, while providing interpretable diagnostics of model compliance.' volume: 337 URL: https://proceedings.mlr.press/v337/baumgartner26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/baumgartner26a/baumgartner26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-baumgartner26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: David family: Baumgartner - given: Eliezer de Souza prefix: da family: Silva - given: Iñigo family: Urteaga editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 448-468 id: baumgartner26a issued: date-parts: - 2026 - 8 - 6 firstpage: 448 lastpage: 468 published: 2026-08-06 00:00:00 +0000 - title: 'Sparse recovery of Diffusion Dynamics: Handling High-Dimensionality in Repeated Short Trajectories' abstract: 'High-dimensional stochastic differential equations encode complex interaction structures within their drift component. We propose a novel approach to estimate this drift from independent high-frequency trajectory data observed over a short time horizon. Each trajectory is modelled as the solution of a Brownian-driven stochastic differential equation, while the number of time points within each path tends to infinity. We further assume that the drift function governing the dynamics can be expressed as a linear combination of a growing number of Lipschitz basis functions. To promote accurate recovery of the underlying dynamics under sparsity constraints, we propose a Lasso-regularised likelihood criterion. Under suitable regularity conditions, we establish convergence rates for the resulting estimator and emphasise how they depend on the dimensional parameters of the problem, in particular on the number of observed trajectories. We assess the performance of the estimator on synthetic datasets, both from an estimation and a generative perspective. Finally, we illustrate the practical relevance of the approach on a real-world climate dataset, highlighting its ability to perform variable selection.' volume: 337 URL: https://proceedings.mlr.press/v337/bayraktar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bayraktar26a/bayraktar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bayraktar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Elise family: Bayraktar - given: Charlotte family: Dion-Blanc editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 469-490 id: bayraktar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 469 lastpage: 490 published: 2026-08-06 00:00:00 +0000 - title: 'Bound to Disagree: Generalization Bounds via Certifiable Surrogates' abstract: 'Generalization bounds for deep learning models are typically vacuous, not computable or restricted to specific model classes. In this paper, we tackle these issues by providing new disagreement-based certificates for the gap between the true risk of any two predictors. We then bound the true risk of the predictor of interest via a surrogate model that enjoys tight generalization guarantees, and by evaluating our disagreement bound on an unlabeled dataset. We empirically demonstrate the tightness of the obtained certificates and showcase the versatility of the approach by training surrogate models leveraging three different frameworks: sample compression, model compression and {PAC-Bayes} theory. Importantly, such guarantees are achieved without modifying the target model, nor adapting the training procedure to the generalization framework.' volume: 337 URL: https://proceedings.mlr.press/v337/bazinet26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bazinet26a/bazinet26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bazinet26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mathieu family: Bazinet - given: Valentina family: Zantedeschi - given: Pascal family: Germain editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 491-520 id: bazinet26a issued: date-parts: - 2026 - 8 - 6 firstpage: 491 lastpage: 520 published: 2026-08-06 00:00:00 +0000 - title: 'Approximation Rates for Schrödinger Bridge Potentials via Fixed-Point ERM' abstract: 'The Schrödinger bridge problem (SBP) provides a principled interpolation between two distributions by selecting, among all path measures matching given endpoint marginals, the one closest in relative entropy to a reference dynamics. In modern applications the marginals are observed only through samples, and standard computational pipelines solve a discretized SBP via {Sinkhorn} iterations and then heuristically extend the resulting dual potentials off-sample, entangling statistical, optimization, and smoothing errors. We study a learning-theoretic alternative based on a fixed-point characterization of a single \emph{transformed} Schrödinger potential $g^\star$, and we focus on quantitative approximation of $g^\star$ by a sample-based estimator $\widehat g$ that is continuous by construction. To address the intrinsic scaling ambiguity of Schrödinger potentials, we introduce a normalized, scale-invariant operator and analyze its local geometry around $g^\star$. Our main theoretical contribution is a stability result linking the error of the fixed-point residual to a distance to the solution $g^\star$ via analysis of spectral-gap property for the {Fréchet} derivative of the operator in a norm $\|\cdot\|$ being the sum of a localized {Hilbert} tangent seminorm and an $L^2$ distance. Combining this stability bound with the excess risk bounds and approximation error yields explicit non-asymptotic rates for $\|\widehat g-g^\star\|$. We illustrate performance of the suggested approach with numerical experiments.' volume: 337 URL: https://proceedings.mlr.press/v337/belomestny26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/belomestny26a/belomestny26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-belomestny26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Denis family: Belomestny - given: Alexey family: Naumov - given: Nikita family: Puchkin - given: Denis family: Suchkov editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 521-548 id: belomestny26a issued: date-parts: - 2026 - 8 - 6 firstpage: 521 lastpage: 548 published: 2026-08-06 00:00:00 +0000 - title: 'Testing Partially-Identifiable Causal Queries Using Ternary Tests' abstract: 'We consider hypothesis testing of binary causal queries using observational data. Since the mapping of causal models to the observational distribution that they induce is not one-to-one, in general, causal queries are often only partially identifiable. When binary statistical tests are used for testing partially-identifiable causal queries, their results do not translate in a straightforward manner to the causal hypothesis testing problem. We propose using ternary (three-outcome) statistical tests to test partially-identifiable causal queries. We establish testability requirements that ternary tests must satisfy in terms of uniform consistency and present equivalent topological conditions on the hypotheses. To leverage the existing toolbox of binary tests, we prove that obtaining ternary tests by combining binary tests is complete. Finally, we demonstrate how topological conditions serve as a guide to construct ternary tests for two concrete causal hypothesis testing problems, namely testing the instrumental variable (IV) inequalities and comparing treatment efficacy.' volume: 337 URL: https://proceedings.mlr.press/v337/bhadane26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bhadane26a/bhadane26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bhadane26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sourbh family: Bhadane - given: Joris M. family: Mooij - given: Philip family: Boeken - given: Onno family: Zoeter editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 549-566 id: bhadane26a issued: date-parts: - 2026 - 8 - 6 firstpage: 549 lastpage: 566 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Weighted Triangulation of Causal Effects Under Model Uncertainty' abstract: 'A fundamental challenge in causal inference with observational data is correct specification of a causal model. When there is model uncertainty, analysts may seek to use estimates from multiple candidate models that rely on distinct, and possibly partially overlapping, sets of identifying assumptions to infer the causal effect, a process known as triangulation. Principled methods for triangulation, however, remain underdeveloped. Here, we develop a framework for causal effect triangulation that combines model testability methods from causal discovery with statistical inference methods from semiparametric theory, while avoiding explicit model selection and post-selection inference problems. We propose a triangulation functional that combines identified functionals from each model with data-driven measures of model validity. We provide a bound on the distance of the functional from the true causal effect along with conditions under which this distance can be taken to zero. Finally, we derive valid statistical inference for this functional. Our framework formalizes robustness under causal pluralism without requiring agreement across models or commitment to a single specification. We demonstrate its performance through simulations and an empirical application.' volume: 337 URL: https://proceedings.mlr.press/v337/bhattacharya26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bhattacharya26a/bhattacharya26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bhattacharya26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Rohit family: Bhattacharya - given: Ina family: Ocelli - given: Ted family: Westling editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 567-584 id: bhattacharya26a issued: date-parts: - 2026 - 8 - 6 firstpage: 567 lastpage: 584 published: 2026-08-06 00:00:00 +0000 - title: 'Algorithm Design and Stronger Guarantees for the Improving Multi-Armed Bandits Problem' abstract: 'The improving multi-armed bandits problem is a formal model for allocating effort under uncertainty, motivated by scenarios such as investing research effort into new technologies, performing clinical trials, and hyperparameter selection from learning curves. Each pull of an arm provides reward that increases monotonically with diminishing returns. A growing line of work has designed algorithms for improving bandits, albeit with somewhat pessimistic worst-case guarantees. Indeed, strong lower bounds of $\Omega(k)$ and $\Omega(\sqrt{k})$ multiplicative approximation factors are known for both deterministic and randomized algorithms (respectively) relative to the optimal arm, where $k$ is the number of bandit arms. In this work, we propose two new parameterized families of bandit algorithms and bound the sample complexity of learning the near-optimal algorithm from each family using offline data. We also perform empirical evaluations on standard hyperparameter tuning benchmarks. The first family we define includes the optimal randomized algorithm from prior work. We show that an appropriately chosen algorithm from this family can achieve stronger guarantees, with optimal dependence on $k$, when the arm reward curves satisfy additional properties related to the strength of concavity. Our second family contains algorithms that both guarantee best-arm identification on well-behaved instances and revert to worst-case guarantees on poorly-behaved instances.' volume: 337 URL: https://proceedings.mlr.press/v337/blum26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/blum26a/blum26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-blum26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Avrim family: Blum - given: Marten family: Garicano - given: Kavya family: Ravichandran - given: Dravyansh family: Sharma editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 585-619 id: blum26a issued: date-parts: - 2026 - 8 - 6 firstpage: 585 lastpage: 619 published: 2026-08-06 00:00:00 +0000 - title: 'Characterising the Convergence of Imprecise Markov Chains' abstract: 'Motivated by their connection to the limit behaviour of imprecise {Markov} chains, we study the asymptotic behaviour of upper transition operators. Our focus is on their convergence: the condition that for every real function, the sequence generated by repeated application of the operator admits a well-defined limit. This notion is strictly weaker than classical ergodicity, which enforces convergence to a constant, and therefore requires a different analytic treatment. We develop a full characterisation of convergence in terms of graph-theoretic relations induced by the operator: accessibility and lower reachability. The resulting criterion is both necessary and sufficient, and applies to arbitrary upper transition operators without structural restrictions, thus strengthening earlier work that provided only sufficient conditions for the unrestricted case.' volume: 337 URL: https://proceedings.mlr.press/v337/de-bock26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/de-bock26a/de-bock26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-de-bock26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jasper family: De Bock - given: Alexander family: Erreygers - given: Floris family: Persiau editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 620-639 id: de-bock26a issued: date-parts: - 2026 - 8 - 6 firstpage: 620 lastpage: 639 published: 2026-08-06 00:00:00 +0000 - title: 'Proximal Policy Optimization Suffices for On-Policy Reinforcement Learning' abstract: 'Proximal Policy Optimization ({PPO}) has been applied to a wide range of applications, from robotics to large language models ({LLMs}). Yet, despite its success, it still suffers from unstable updates, performance collapse, and extreme sensitivity to hyperparameters. Many alternatives have been proposed to alleviate these issues, often demonstrating empirically stronger performance on standard reinforcement learning ({RL}) benchmarks. In this work, we observe that {PPO}’s training instability fundamentally stems from the brittle inter-coupling between its surrogate optimization hyperparameters which jointly dictate the effective size of policy updates. This complex coupling makes tuning quite difficult and, in practice, often leaves {PPO} under-performing. To mitigate this, we introduce a criterion on trajectories generated by behavior and target policies which can be used as an early stopping rule. This formulation effectively decouples the optimization dynamics, allowing the algorithm to adaptively scale its updates using a single threshold parameter. We additionally find a scaling law between this threshold parameter and the number of trajectory batches collected, further reducing the tuning burden. Using this simple criterion, we evaluate {PPO} on continuous control tasks from the {DM} Control Suite, outperforming prior policy gradient methods and revealing that many reported improvements were largely artifacts of under-performing {PPO} baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/bouftini26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bouftini26a/bouftini26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bouftini26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Rayane family: Bouftini - given: Mohammed family: Benzaouia editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 640-657 id: bouftini26a issued: date-parts: - 2026 - 8 - 6 firstpage: 640 lastpage: 657 published: 2026-08-06 00:00:00 +0000 - title: 'Pareto-Optimal Probabilistic Explanations: Balancing Cognitive Constraints and User Preferences' abstract: 'Machine learning classifiers deployed in critical domains require comprehensible explanations. Abductive explanations identify minimal feature sets guaranteeing a decision but suffer from two limitations: exceeding human cognitive limits and ignoring user preferences (actionability, fairness, cost). Probabilistic explanations reduce size via controlled error, while preferred explanations integrate preferences; however, these approaches remain disjoint. We introduce the first framework unifying these paradigms: preferred probabilistic explanations balancing cognitive constraints, probabilistic accuracy, and user preferences. We formulate the problem via weighted scalarization **WPPE** and Pareto optimization PPPE, prove **NP**-hardness for decision trees, and exploit supermodularity to establish approximation guarantees. We propose three complementary algorithms: weighted greedy descent **WGD** with ratio $(e^{p_w}-1)/p_w$, Pareto frontier enumeration **PFE** for interactive exploration of non-dominated trade-offs, and lexicographic stratified algorithm **LSA** for strict ordinal preferences. Our framework enables rigorous navigation of the Pareto-optimal trade-off space between cognitive limits and user preferences.' volume: 337 URL: https://proceedings.mlr.press/v337/bounia26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bounia26a/bounia26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bounia26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Louenas family: Bounia editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 658-688 id: bounia26a issued: date-parts: - 2026 - 8 - 6 firstpage: 658 lastpage: 688 published: 2026-08-06 00:00:00 +0000 - title: 'Fundamental Limits and Optimal Methods for Sharp Analytical Causal Bounds in Instrumental Variable Models' abstract: 'Bounding causal effects analytically, rather than numerically, is appealing for its interpretability and conceptual clarity. Existing sharp methods rely on optimization-based approaches such as the Balke–{Pearl} framework, whose computational complexity grows rapidly. An alternative line of work derives bounds heuristically using probability laws and generic inequalities, and some recent papers have claimed or conjectured that this approach can yield sharp analytical bounds with substantially lower complexity. In this paper, we show that this perceived advantage is illusory. In particular, in a discrete instrumental variable setting, we show that any sharp analytical bound for the average treatment effect must be expressible as a maximum (minimum) over a collection of linear terms whose cardinality grows exponentially in the number of values taken by the outcome. In parallel, we show that the number of instrumental variable inequalities itself also grows exponentially. Consequently, bounds and inequalities expressed using only polynomially many such terms cannot be sharp. As a constructive complement, the paper is accompanied by codes implemented in python and R to derive sharp analytical bounds and sharp inequalities with optimal computational complexity, matching the lower bounds proven in this paper. These codes are available \href{https://github.com/ArefeBoushehrian/Analytical-Causal-Bounds-in-Instrumental-Variable-Models}{online}.' volume: 337 URL: https://proceedings.mlr.press/v337/boushehrian26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/boushehrian26a/boushehrian26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-boushehrian26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Arefe family: Boushehrian - given: Mohammad Reza family: Badri - given: Sina family: Akbari - given: Negar family: Kiyavash editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 689-744 id: boushehrian26a issued: date-parts: - 2026 - 8 - 6 firstpage: 689 lastpage: 744 published: 2026-08-06 00:00:00 +0000 - title: 'Bayesian Symbolic Regression with Entropic Reinforcement Learning' abstract: 'Symbolic regression is the problem of finding an algebraic expression describing a stochastic dependence of a target variable on a set of inputs. Unlike forms of regression that fit parameters assuming a fixed model structure, symbolic regression is a search problem over the space of expressions, represented, for example, as abstract syntax trees using a library of operators. Symbolic regression is typically used in settings with limited, noisy data in the natural sciences. However, searching for a single best-fitting expression fails to capture the epistemic uncertainty about the expression, which motivates a {Bayesian} perspective that enables uncertainty quantification and specification of natural priors to constrain the search space. In this work, we propose {ERRLESS} (Entropy-Regularized Reinforcement Learning for Expression Structure Sampling), a scalable approach for sampling from the posterior distribution over expressions given data using maximum-entropy reinforcement learning. {ERRLESS} learns a neural policy that constructs expressions sequentially by building up their abstract syntax trees. At convergence, the policy samples expressions from the posterior. At test time, expressions can be sampled by rollouts of this policy. We demonstrate that {ERRLESS} achieves competitive results on the {Feynman} benchmark while producing short and interpretable expressions. Additionally, we demonstrate that the mean of the posterior predictive approximated by {ERRLESS} achieves a high coefficient of determination ($R^2$) compared to an SMC baseline, highlighting the benefits of the {Bayesian} perspective in symbolic regression.' volume: 337 URL: https://proceedings.mlr.press/v337/boussif26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/boussif26a/boussif26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-boussif26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Oussama family: Boussif - given: Mohammed family: Mahfoud - given: Younesse family: Kaddar - given: Moksh family: Jain - given: Sida family: Li - given: Damiano family: Fornasiere - given: Xiaoyin family: Chen - given: Yoshua family: Bengio - given: Esmeralda S. family: Whitammer editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 745-764 id: boussif26a issued: date-parts: - 2026 - 8 - 6 firstpage: 745 lastpage: 764 published: 2026-08-06 00:00:00 +0000 - title: 'Task Expansion and Cross Refinement for Open-World Conditional Modeling' abstract: 'Open-world conditional modeling (OCM), requires a single model to answer arbitrary conditional queries across heterogeneous datasets, where observed variables and targets vary and arise from a vast open-ended task universe. Because any finite collection of real-world datasets covers only a small fraction of this space, we propose Task Expansion and Cross Refinement ({TEXR}), a semi-supervised framework that enlarges effective task coverage through structured synthesis and refinement of semantic data contexts. {TEXR} first generates diverse uninstantiated dataset schemas and weakly instantiates them via structured probabilistic generators guided by large language models. It then performs cross-model refinement by training on disjoint data partitions and revising synthetic values across splits to reduce confirmation bias and improve pseudo-value quality. The refined synthetic datasets are aggregated with real data to train a unified conditional model. Across heterogeneous tabular benchmarks, {TEXR} consistently improves zero-, few-, and many-shot performance for multiple OCM backbones, demonstrating that structured task expansion and cross refinement enhance open-world conditional modeling.' volume: 337 URL: https://proceedings.mlr.press/v337/brahmavar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/brahmavar26a/brahmavar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-brahmavar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shreyas Bhat family: Brahmavar - given: Qiyang family: Liu - given: Yang family: Li - given: Junier family: Oliva editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 765-784 id: brahmavar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 765 lastpage: 784 published: 2026-08-06 00:00:00 +0000 - title: 'Causal Discovery with Metadata-Informed Latent Types' abstract: 'Causal discovery seeks to recover causal structure from data but the underlying graph is typically identifiable only up to its {Markov} equivalence class. Yet real-world systems often exhibit redundancy, where groups of variables share similar causal roles. We introduce a {Bayesian} causal discovery framework that leverages variable-level metadata to infer latent types and constrain causal interactions across variables. We model causal graphs as type-consistent DAGs and propose t-{DiBS}, a fully differentiable method that jointly learns variable types, graph structure, and metadata representations. Our approach enables principled uncertainty quantification and integrates expressive neural models for metadata. We provide theoretical results showing that, under structured assumptions, metadata combined with typing can improve identifiability beyond classical limits. Empirically, we demonstrate improved performance over standard causal discovery methods on synthetic and pseudo-real datasets, with detailed analysis demonstrating the benefit of joint type and structure learning. These results establish metadata-driven typing as a principled approach to identifiable causal discovery.' volume: 337 URL: https://proceedings.mlr.press/v337/brouillard26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/brouillard26a/brouillard26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-brouillard26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Philippe family: Brouillard - given: Alexandre family: Drouin - given: Dhanya family: Sridhar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 785-818 id: brouillard26a issued: date-parts: - 2026 - 8 - 6 firstpage: 785 lastpage: 818 published: 2026-08-06 00:00:00 +0000 - title: 'Model Merging as Probabilistic Inference in Fine-Tuning Parameter Space' abstract: 'Model merging aims to combine existing single-task solutions into a multi-task solution without additional data-driven fine-tuning. Most existing approaches achieve this using geometric properties of local solution spaces. However, such geometric views provide limited guidance for scoring how statistically useful each task-specific update direction is across tasks during merging. To address this, we formulate model merging from a new perspective of probabilistic inference under a product-of-experts ({PoE}) scenario where each single-task solution defines an energy-based expert model ({EBM}) over the merged parameters. We show that several existing model merging methods arise as special cases of our framework under energy designs that impose implicit {Gaussian} assumptions on directional residuals between merged and task-specific models. Empirically, we find that these residuals are often heavy-tailed which exposes a mismatch with the imposed light-tailed {Gaussian} structures. We address this with a heavy-tailed {PoE} design based on {Cauchy} experts, which better captures the observed residual behavior while admitting a provably convergent inference procedure. Experiments across multiple tasks and architectures show significant improvements over state-of-the-arts baselines. Our code is available at https://github.com/MinhLong210/{PoE}-{EBM}-Merging.git.' volume: 337 URL: https://proceedings.mlr.press/v337/bui26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bui26a/bui26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bui26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Long Minh family: Bui - given: Tuan Anh Le family: Van - given: Tung Phi family: Duc - given: Phi Le family: Nguyen - given: Jana family: Doppa - given: Trong Nghia family: Hoang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 819-838 id: bui26a issued: date-parts: - 2026 - 8 - 6 firstpage: 819 lastpage: 838 published: 2026-08-06 00:00:00 +0000 - title: 'Uncertainty Quantification for Regression: A Unified Framework based on kernel scores' abstract: 'Regression tasks, notably in safety-critical domains, require reliable uncertainty quantification, yet the literature remains largely classification-focused. To address this, we introduce a family of measures for total, aleatoric, and epistemic uncertainty in multivariate regression based on strictly proper kernel scores. The framework provides a principled recipe for designing new uncertainty measures whose behavior, such as tail sensitivity or out-of-distribution responsiveness, is governed by the choice of the underlying kernel, while also encompassing existing measures under a joint analysis. We prove explicit correspondences between properties of the kernel and behavior of resulting uncertainty measures, yielding concrete design guidelines for practitioners. Extensive experiments across structured regression tasks, including spatial and functional domains, demonstrate effectiveness on downstream tasks such as out-of-distribution detection and active learning, and reveal that different kernel choices lead to distinct trade-offs, offering practitioners guidance for task-specific selection.' volume: 337 URL: https://proceedings.mlr.press/v337/bulte26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bulte26a/bulte26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bulte26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Christopher family: Bülte - given: Yusuf family: Sale - given: Gitta family: Kutyniok - given: Eyke family: Hüllermeier editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 839-879 id: bulte26a issued: date-parts: - 2026 - 8 - 6 firstpage: 839 lastpage: 879 published: 2026-08-06 00:00:00 +0000 - title: 'An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression' abstract: 'Uncertainty quantification is crucial in machine learning, yet most (axiomatic) studies of uncertainty measures focus on classification, leaving a gap in regression settings with limited formal justification and evaluations. In this work, we provide a formal way of representing uncertainty in continuous space, using a general parametric formulation, allowing for tractable analysis and evaluation of uncertainty measures. Within this framework, we propose a set of axioms that enable rigorous assessment of total, aleatoric, and epistemic uncertainty measures. Together, this allows for a theoretical examination of uncertainty measures and their corresponding properties. As a specific example, we compare the widely used entropy- and variance-based measures with respect to established predictive models and analyze their limitations and challenges in uncertainty quantification. Our work provides a principled way to understand and develop uncertainty measures in supervised regression, offering theoretical insights and practical guidelines for reliable uncertainty assessment.' volume: 337 URL: https://proceedings.mlr.press/v337/bulte26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/bulte26b/bulte26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-bulte26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Christopher family: Bülte - given: Yusuf family: Sale - given: Timo family: Löhr - given: Paul family: Hofman - given: Gitta family: Kutyniok - given: Eyke family: Hüllermeier editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 880-899 id: bulte26b issued: date-parts: - 2026 - 8 - 6 firstpage: 880 lastpage: 899 published: 2026-08-06 00:00:00 +0000 - title: 'Provably Efficient Personalized Multi-Objective Bandits with Proactive Conversational Queries' abstract: 'Personalized decision-making in multi-objective bandits requires learning user-specific trade-offs among competing objectives. Since arm utility depends on both unknown rewards and unknown preferences, existing methods infer preferences only from utility feedback, entangling preference learning with reward exploration. In practice, however, users often reveal their priorities through proactive conversational queries (e.g., “cheap and clean hotel”), yet this structured signal is not leveraged. We formalize a proactive query-based framework in which user queries provide structured preference signals. Modeling these signals via a Plackett–Luce subset choice model, we show that query-only learning is insufficient due to a fundamental shift-invariance barrier. To resolve this, we introduce MO-PQUCB, a hybrid algorithm that integrates query-based preference anchoring with bandit feedback through shift-invariant regularization and dual-exploration {UCB}. We prove that proactive queries accelerate preference estimation and yield improved regret scaling over prior preference-aware MO-MAB methods. Under corrupted queries, we further characterize statistical limits and design a robust estimator achieving near-optimal performance when corruption is sparse. Experiments validate both theoretical and practical gains.' volume: 337 URL: https://proceedings.mlr.press/v337/cao26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/cao26a/cao26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-cao26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Linfeng family: Cao - given: Ming family: Shi - given: Ness family: Shroff editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 900-942 id: cao26a issued: date-parts: - 2026 - 8 - 6 firstpage: 900 lastpage: 942 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Features' abstract: 'We propose a robust {Bayesian} formulation of random feature (RF) regression that accounts explicitly for prior and likelihood misspecification via {Huber}-style contamination sets. Starting from the classical equivalence between ridge-regularized RF training and {Bayesian} inference with {Gaussian} priors and likelihoods, we replace the single prior and likelihood with $\epsilon$- and $\eta$-contaminated credal sets, respectively, and perform inference using pessimistic generalized {Bayesian} updating. We derive explicit and tractable bounds for the resulting lower and upper posterior predictive densities. These bounds show that, when contamination is moderate, prior and likelihood ambiguity effectively acts as a direct contamination of the posterior predictive distribution, yielding uncertainty envelopes around the classical {Gaussian} predictive. We introduce an Imprecise Highest Density Region ({IHDR}) for robust predictive uncertainty quantification and show that it admits an efficient outer approximation via an adjusted {Gaussian} credible interval. We further obtain predictive variance bounds (under a mild truncation approximation for the upper bound) and prove that they preserve the leading-order proportional-growth asymptotics known for RF models. Together, these results establish a robustness theory for {Bayesian} random features: predictive uncertainty remains computationally tractable, inherits the classical double-descent phase structure, and is improved by explicit worst-case guarantees under bounded prior and likelihood misspecification.' volume: 337 URL: https://proceedings.mlr.press/v337/caprio26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/caprio26a/caprio26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-caprio26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Michele family: Caprio - given: Katerina family: Papagiannouli - given: Siu Lun family: Chau - given: Sayan family: Mukherjee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 943-960 id: caprio26a issued: date-parts: - 2026 - 8 - 6 firstpage: 943 lastpage: 960 published: 2026-08-06 00:00:00 +0000 - title: 'Neural Routed Boosting: Robust Learning against Heteroscedastic Noise' abstract: 'Boosting algorithms such as AdaBoost have achieved widespread success by iteratively focusing on hard-to-classify instances. However, this aggressive re-weighting mechanism makes them susceptible to label noise and overfitting. While robust variants like Conditional Boosting handle this by estimating conditional risk, they rely on global statistical approximations. We propose Neural Routed Boosting, a novel ensemble framework that addresses heteroscedastic noise through a structural approach. Neural Routed Boosting utilizes a lightweight neural network to partition the input space into geometrically coherent regions, training specialized weak learners for each. This isolates noisy subspaces, preventing them from corrupting the decision boundaries of clean regions. We prove that the composite model of a neural router and region-specific experts constitutes a valid weak learner under the boosting framework, guaranteeing training error convergence. Experimental results on synthetic and real-world datasets demonstrate that Neural Routed Boosting outperforms traditional and robust boosting baselines, including Conditional Boosting, in high-noise environments.' volume: 337 URL: https://proceedings.mlr.press/v337/chakraborty26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chakraborty26a/chakraborty26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chakraborty26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Puspak family: Chakraborty - given: Arun family: Rajkumar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 961-980 id: chakraborty26a issued: date-parts: - 2026 - 8 - 6 firstpage: 961 lastpage: 980 published: 2026-08-06 00:00:00 +0000 - title: 'Group-Fair Allocations of Contiguous Blocks of Indivisible Items' abstract: 'We study the problem of allocating contiguous blocks of indivisible items positioned on a line to a set of agents where agents are partitioned into different groups. In the problem, agents must be located on a line, and items allocated to each agent must be contiguous and form a connected block. We study the settings, considered by Suksompong [2019] and Wang et al. [2021], without and with the requirement that items are assigned to their closest agents, respectively. For both settings, we focus on allocations that satisfy intra-group envy fairness (IEF) and inter-group fair share (GFS). In both settings, we show that determining the existence of IEF or GFS allocations is NP-complete. When the number of agents or items is constant, we provide polynomial algorithms to determine the existence of IEF or GFS allocations for both settings. For both settings, we provide upper and lower bounds on the existence of IEF or GFS allocations as well as allocations that satisfy both IEF and GFS simultaneously.' volume: 337 URL: https://proceedings.mlr.press/v337/chan26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chan26a/chan26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chan26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hau family: Chan - given: Minming family: Li - given: Yingchao family: Zhao - given: Shangkun family: Zheng editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 981-1002 id: chan26a issued: date-parts: - 2026 - 8 - 6 firstpage: 981 lastpage: 1002 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Constrained Markov Games: Multi-Agent Decision-Making under Model Uncertainty and Constraints' abstract: 'Multi-agent decision-making under both uncertainty and constraints is a central challenge in safety-critical domains such as autonomous driving, where agents must coordinate in uncertain environments while ensuring feasibility with respect to safety and resource limits. However, there is limited theoretical and practical work that addresses this challenge. Therefore, we introduce a Robust Constrained {Markov} Game (RCMG), the first multi-agent framework that simultaneously captures adversarial transition uncertainty and cost constraints. We further propose a solution concept, the Robust and Feasible {Nash} Equilibrium (RFNE), and a principled relaxation that yields a tractable surrogate upper bound to the intractable problem of computing an exact RFNE. This surrogate enables both a fixed-point existence proof via {Kakutani}’s theorem and a decentralized algorithm that alternates robust dynamic programming with Lagrangian dual updates. In settings where the relaxation is tight, the method provably recovers an exact RFNE. A grid-world experiment illustrates consistency with the theoretical results and highlights the viability of RCMGs as a foundation for reliable multi-agent decision-making under uncertainty and constraints.' volume: 337 URL: https://proceedings.mlr.press/v337/chang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chang26a/chang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ningkang family: Chang - given: Chenyu family: Xu - given: Ziying family: Jia - given: Yue family: Wang - given: Sihong family: He editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1003-1033 id: chang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1003 lastpage: 1033 published: 2026-08-06 00:00:00 +0000 - title: 'Inference for quantile-parametrized families via CDF confidence bands' abstract: 'Quantile-based distribution families are an important subclass of parametric families, capable of exhibiting a wide range of behaviors using very few parameters. These parametric models present significant challenges for classical methods, since the CDF and density do not have a closed-form expression. Furthermore, approximate maximum likelihood estimation and related procedures may yield non-$\sqrt{n}$ and non-normal asymptotics over regions of the parameter space, making bootstrap and resampling techniques unreliable. We develop a novel inference framework that constructs confidence sets by inverting distribution-free confidence bands for the empirical CDF through the known quantile function. Our proposed inference procedure provides a principled and assumption-lean alternative in this setting, requiring no distributional assumptions beyond the parametric model specification and avoiding the computational and theoretical difficulties associated with likelihood-based methods for these complex parametric families. We demonstrate our framework on {Tukey} {Lambda} and generalized {Lambda} distributions, evaluate performance through simulation studies, and illustrate practical utility with applications to a small-sample dataset (Twin Study) and a large-sample dataset ({Spanish} household incomes).' volume: 337 URL: https://proceedings.mlr.press/v337/chattopadhyay26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chattopadhyay26a/chattopadhyay26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chattopadhyay26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Srijan family: Chattopadhyay - given: Siddhaarth family: Sarkar - given: Arun K. family: Kuchibhotla editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1034-1053 id: chattopadhyay26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1034 lastpage: 1053 published: 2026-08-06 00:00:00 +0000 - title: 'Linear Regression with Heteroskedastic Errors' abstract: 'We study the classic linear regression problem under the challenging setting of heteroskedastic noise. We study a model in which we have $n$ sources that each observe linear measurements of an unknown $d$-dimensional vector $\beta$. Each source has an unknown and distinct variance for the error, and the goal is to estimate the parameter vector $\beta$, under the assumption that there exist \emph{sufficiently many} sources with small error (specifically, $m$ sources have variance at most $1$). Our results show that $\beta$ can be estimated to sub-constant error, as long as the number of small-error sources, i.e., $m$, is large enough. We prove two main results. First, we show that even with just one observation per source, under minimal assumptions on the linear measurements, $\beta$ can be estimated to sub-constant error when $m \ge n^{1- \frac{1}{4d}}$. Second, we show that if we have access to \emph{two} observations per source, under similar assumptions on the linear measurements, $\beta$ can be estimated to sub-constant error when $m \ge n^{5/6}$. Our results are related to the recent line of work on mean estimation with heteroskedastic variances, and more specifically, the \emph{subset of signals} model used in this literature. To the best of our knowledge, our results provide the first sub-constant recovery guarantees for regression in this model.' volume: 337 URL: https://proceedings.mlr.press/v337/chaudhary26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chaudhary26a/chaudhary26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chaudhary26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Siddhant family: Chaudhary - given: Aditya family: Bhaskara editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1054-1080 id: chaudhary26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1054 lastpage: 1080 published: 2026-08-06 00:00:00 +0000 - title: 'SteinGate: Tail-Sensitive Safe Reinforcement Learning via Stein Discrepancy' abstract: 'Safe reinforcement learning typically enforces safety by bounding expected cumulative costs, a criterion that often fails to detect rare but catastrophic tail events. To overcome these limitations, this paper introduces {\em {SteinGate}}, a boundary-aware distributional safety certificate that replaces fragile tail fitting with a robust consistency check using Kernelized {Stein} Discrepancy while accounting for boundary atoms induced by clipped costs. {SteinGate} evaluates whether observed policy rollout costs remain consistent with a safe reference distribution, providing a non-parametric safety certificate. This certificate is used to dynamically adapt the learning regime: favoring reward-improving policy updates when rollouts remain consistent with the safe reference and switching to recovery behavior when the cost tail deviates. Experiments on continuous-control benchmarks demonstrate that {SteinGate} significantly reduces both the frequency and severity of constraint violations during training while maintaining competitive returns relative to state-of-the-art baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/chemingui26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chemingui26a/chemingui26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chemingui26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yassine family: Chemingui - given: Chenhua family: Fan - given: Honghao family: Wei - given: Janardhan Rao family: Doppa editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1081-1104 id: chemingui26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1081 lastpage: 1104 published: 2026-08-06 00:00:00 +0000 - title: 'Interactive Multi-Objective Probabilistic Preference Learning with Soft and Hard Bounds' abstract: 'High-stakes decision-making involves navigating multiple competing objectives with expensive evaluations. For instance, in brachytherapy, clinicians must balance maximizing tumor coverage (e.g., an aspirational target or soft bound of $>$95% coverage) against strict organ dose limits (e.g., a non-negotiable hard bound of $<$601 cGy to the bladder). Selecting Pareto-optimal solutions that match implicit preferences is challenging, as exhaustive Pareto frontier exploration is computationally and cognitively prohibitive, necessitating interactive frameworks to guide users. While decision-makers (DMs) often possess domain knowledge to narrow the search via such soft-hard bounds, current methods often lack systematic approaches to iteratively refine these multi-faceted preference structures. Furthermore, DMs often require confidence that they have not overlooked superior alternatives, a paramount necessity in high-stakes scenarios. We present Active-{MoSH}, an interactive local-global framework designed for this process. Its local component integrates probabilistic preference learning with an active sampling strategy to adaptively refine Pareto subsets while minimizing cognitive burden. To bolster decision confidence, Active-{MoSH}’s global component, C-{MoSH}, leverages multi-objective sensitivity analysis to identify potentially overlooked, high-value points beyond immediate feedback. We demonstrate Active-{MoSH}’s performance benefits through diverse synthetic and real-world applications. A high-stakes case study with real cervical cancer brachytherapy treatment plans and an image selection user study further validate our hypotheses regarding the framework’s ability to improve convergence, enhance {DM} confidence, and provide expressive preference articulation.' volume: 337 URL: https://proceedings.mlr.press/v337/chen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chen26a/chen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Edward family: Chen - given: Sang T. family: Truong - given: Natalie family: Dullerud - given: Sanmi family: Koyejo - given: Carlos family: Guestrin editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1105-1153 id: chen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1105 lastpage: 1153 published: 2026-08-06 00:00:00 +0000 - title: 'Finite-Sample Regret Analysis of Nash Q-Learning with Random-Feature Approximation' abstract: 'We study finite-sample equilibrium learning in episodic two-player zero-sum {Markov} games, where {Nash} equilibria coincide with minimax saddle points and {Nash}-Q style value iteration provides a natural algorithmic template. Existing analyses of {Nash}-Q style learning provide regret guarantees in tabular settings and under fixed linear realizability, but do not explicitly account for representation error arising from scalable nonlinear approximation. We propose an optimistic {Nash} Q-learning framework that replaces tabular/linear value representations with a hyperdimensional random-feature embedding—instantiated via random {Fourier} features to approximate a shift-invariant kernel—while retaining tractable ridge-style updates and per-state minimax stage-game computation. Our main results establish high-probability regret guarantees that decompose into a statistical uncertainty term governed by an effective-dimension complexity measure and an explicit additive approximation term induced by random-feature kernel approximation. The approximation term decreases with the embedding dimension, yielding a principled approximation–estimation tradeoff and recovering linear-style finite-sample behavior in the realizable regime. Empirically, we evaluate on a suite of episodic zero-sum benchmarks spanning tabular and continuous-state settings and observe stable learning behavior and performance trends consistent with the predicted dependence on representation dimension.' volume: 337 URL: https://proceedings.mlr.press/v337/chen26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chen26b/chen26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chen26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yongshan family: Chen - given: Yuchen family: Hou - given: Zhuowen family: Zou - given: Calvin family: Yeung - given: Mohsen family: Imani - given: Tian family: Lan - given: Mahdi family: Imani editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1154-1180 id: chen26b issued: date-parts: - 2026 - 8 - 6 firstpage: 1154 lastpage: 1180 published: 2026-08-06 00:00:00 +0000 - title: 'On the Granularity of Causal Effect Identifiability' abstract: 'The classical notion of causal effect identifiability is defined in terms of treatment and outcome variables. In this paper, we consider the identifiability of state-based causal effects: how an intervention on a particular _state_ of treatment variables affects a particular _state_ of outcome variables. We demonstrate that state-based causal effects may be identifiable even when variable-based causal effects may not. Moreover, we show that this separation occurs only when additional knowledge — such as context-specific independencies — is available. We further examine knowledge that constrains the states of variables, and show that such knowledge can improve both variable-based and state-based identifiability when combined with other knowledge such as context-specific independencies. We finally propose an approach for identifying causal effects under these additional constraints, and conduct empirical studies to further illustrate the separations between the two levels of identifiability.' volume: 337 URL: https://proceedings.mlr.press/v337/chen26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chen26c/chen26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chen26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yizuo family: Chen - given: Adnan family: Darwiche editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1181-1199 id: chen26c issued: date-parts: - 2026 - 8 - 6 firstpage: 1181 lastpage: 1199 published: 2026-08-06 00:00:00 +0000 - title: 'On the Sublinear Regret of Continuous K-Max Bandits' abstract: 'The $K$-Max combinatorial multi-armed bandit problem arises in applications such as recommendation and distributed decision making, where the reward is determined by the maximum outcome among $K$ selected arms. When outcomes are continuous and only the maximum value together with the winner’s index is observed, this problem introduces unprecedented difficulties including discretization errors, non-deterministic tie-breaking, and severe estimation biases. To overcome these barriers, we introduce DCK-{UCB}, an efficient algorithm combining adaptive discretization with bias-corrected confidence bounds. We prove that DCK-{UCB} achieves a $\widetilde{\mathcal{O}}(T^{3/4})$ regret bound, the first sublinear guarantee in this setting. Numerical experiments show its superior performance over baseline methods. Furthermore, for the specific case of exponential distributions under full-bandit feedback, we propose MLE-Exp algorithm that attains a near-optimal $\widetilde{\mathcal{O}}(\sqrt{T})$ regret bound. This work establishes fundamental theoretical guarantees and provides a powerful algorithmic solution for continuous combinatorial bandits.' volume: 337 URL: https://proceedings.mlr.press/v337/chen26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chen26d/chen26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chen26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yu family: Chen - given: Siwei family: Wang - given: Longbo family: Huang - given: Wei family: Chen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1200-1229 id: chen26d issued: date-parts: - 2026 - 8 - 6 firstpage: 1200 lastpage: 1229 published: 2026-08-06 00:00:00 +0000 - title: 'Hyperbolic Belief Propagation' abstract: 'Belief Propagation (BP) has operated in {Euclidean} space for four decades, yet the polynomial volume growth of $\mathbb{R}^d$ is fundamentally mismatched to hierarchical graphs: faithful embedding of exponentially branching structure demands $d = \Omega(\log n)$ dimensions and prohibitive $\mathcal{O}(d^3)$ covariance costs, while truncating $d$ corrupts marginal estimates. We introduce Continuous Hyperbolic Belief Propagation ({CHBP}), formulated natively on the Lorentz hyperboloid $\mathbb{H}^n_K$, whose exponential volume growth eliminates this bottleneck. {CHBP} parameterises beliefs as Jacobian-corrected Wrapped Normals, approximates message integrals via Gauss–{Hermite} quadrature, and transports covariance tensors between tangent spaces via closed-form Levi-Civita parallel transport, with a curvature annealing schedule ensuring stable convergence. On hierarchical graphs, {CHBP} at $d{=}5$ reduces marginal KL divergence by $25\times$ versus {Euclidean} BP at $d{=}50$ and achieves up to 91.45% accuracy on real-world taxonomies, outperforming all baselines including Hyperbolic GCNs. On flat topologies, {CHBP} predictably underperforms {Euclidean} methods, confirming a topology-specific rather than universal advantage.' volume: 337 URL: https://proceedings.mlr.press/v337/cheng26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/cheng26a/cheng26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-cheng26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zehua family: Cheng - given: Wei family: Dai - given: Jiahao family: Sun editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1230-1248 id: cheng26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1230 lastpage: 1248 published: 2026-08-06 00:00:00 +0000 - title: 'Policy Optimization for Adversarial Linear Mixture MDPs with Unknown Transitions and Bandit Feedback' abstract: 'We study episodic reinforcement learning with adversarial losses and bandit feedback in {MDPs} with unknown transitions under a linear-mixture model. In this setting, prior studies are typically built upon global optimization methods with the notion of occupancy measure, rather than the purely local policy optimization-based method, which avoids solving a constrained convex optimization problem and is thus more preferred in practice. In this work, we develop the first policy optimization-based algorithm that runs online mirror descent locally on each state. The main challenge is to interface local updates with transition learning: the dilated-bonus analysis requires predictable reachability surrogates and robust one-step maximizations over a confidence set, but the statistically natural VLS confidence region is a coupled ellipsoid over a shared parameter and is not $(s,a)$-rectangular. We address this by rectangularizing the VLS ellipsoid into local per-$(s,a)$ kernel sets, which enables robust dynamic programming to compute occupancy envelopes and to drive the implicit-exploration estimator and dilated bonuses. Based on this technique, we prove a high-probability regret bound $\widetilde{\mathcal{O}}\big(H^{3/2}\sqrt{S AK} + dH^{3/2} S^{3/2}\sqrt{K}\big)$, which nearly matches the best-known bound achieved by occupancy-measure-based methods.' volume: 337 URL: https://proceedings.mlr.press/v337/cheng26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/cheng26b/cheng26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-cheng26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yutian family: Cheng - given: Canzhe family: Zhao - given: Shuai family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1249-1270 id: cheng26b issued: date-parts: - 2026 - 8 - 6 firstpage: 1249 lastpage: 1270 published: 2026-08-06 00:00:00 +0000 - title: 'Fairness under Graph Uncertainty: Achieving Interventional Fairness with Partially Known Causal Graphs over Clusters of Variables' abstract: 'Algorithmic decisions about individuals require predictions that are not only accurate but also fair with respect to sensitive attributes such as gender and race. Causal notions of fairness align with legal requirements, yet many methods assume access to detailed knowledge of the underlying causal graph, which is a demanding assumption in practice. We propose a learning framework that achieves interventional fairness by leveraging a causal graph over *clusters of variables*, which is substantially easier to estimate than a variable-level graph. With possible *adjustment cluster sets* identified from such a cluster causal graph, our framework trains a prediction model by reducing the worst-case discrepancy between interventional distributions across these sets. To this end, we develop a computationally efficient barycenter kernel maximum mean discrepancy (MMD) that scales favorably with the number of sensitive attribute values. Extensive experiments show that our framework strikes a better balance between fairness and accuracy than existing approaches, highlighting its effectiveness under limited causal graph knowledge.' volume: 337 URL: https://proceedings.mlr.press/v337/chikahara26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chikahara26a/chikahara26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chikahara26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yoichi family: Chikahara editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1271-1301 id: chikahara26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1271 lastpage: 1301 published: 2026-08-06 00:00:00 +0000 - title: 'Canonical Domain Reduction for Partial Counterfactual Identification' abstract: 'Many counterfactual and causal queries are only partially identified from data, especially under unmeasured confounding. A common approach represents compatible nonparametric structural causal models (SCMs) on a finite canonical domain and computes sharp bounds via linear programming (LP) over the induced simplex. However, the canonical full counterfactual state space grows exponentially even for small graphs, making naive LP-based bounding computationally heavy. We propose a constraint-aware reduction that quotients out degrees of freedom irrelevant to the optimization problem. Because sharp bounds are determined jointly by the query functional and the data-implied information set, we aggregate full states into equivalence classes that are indistinguishable to every linear functional appearing in the LP objective and constraints. We show that optimizing over the induced push-forward distribution on the reduced domain preserves feasibility and yields the same sharp bounds as the full-domain.' volume: 337 URL: https://proceedings.mlr.press/v337/choe26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/choe26a/choe26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-choe26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yesong family: Choe - given: Yeahoon family: Kwon - given: Min Woo family: Park - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1302-1326 id: choe26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1302 lastpage: 1326 published: 2026-08-06 00:00:00 +0000 - title: 'Which Directions Matter? Sparse Design for Affine Robust Optimization' abstract: 'Robust machine learning and optimization rely on the uncertainty model choice. We investigate which uncertainty directions a model must cover when defined by a finite dictionary and a budget constraint. Selecting a subset forms an atomic uncertainty set with a closed form support function, yielding tractable robust programs for affine objectives. We propose a data-driven selection rule based on a coverage objective over evaluation directions, including gradients, adversarial perturbations, or shifts observed on held out data. We prove this objective is monotone and submodular, supporting a greedy method with a $(1-1/e)$ approximation guarantee and a matching hardness barrier. We also provide a certificate bounding the loss from the selected subset and a radius calibration rule with out-of-sample control.' volume: 337 URL: https://proceedings.mlr.press/v337/chumpitaz-flores26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/chumpitaz-flores26a/chumpitaz-flores26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-chumpitaz-flores26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Pedro family: Chumpitaz-Flores - given: My family: Duong - given: Juan S. family: Borrero - given: Kaixun family: Hua editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1327-1356 id: chumpitaz-flores26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1327 lastpage: 1356 published: 2026-08-06 00:00:00 +0000 - title: 'Ensemble Diversity Optimization for Subjective Supervision' abstract: 'Subjective NLP tasks often exhibit systematic annotator disagreement, requiring models that represent uncertainty rather than collapse it. We introduce Ensemble Diversity Optimization (EDO), a prediction-space framework that jointly optimizes ensemble weights, effective cardinality, and calibration through a unified differentiable objective. EDO learns ensemble composition and size end-to-end via Gumbel–Softmax relaxation and incorporates a signed diversity regularizer, tuned on validation data, to steer optimization toward either preserving or suppressing disagreement. This regularization prevents ensemble collapse and enables controlled navigation of the utility–calibration trade-off. The framework integrates a soft F1 surrogate, class-weighted cross-entropy to address imbalance, and reliability-weighted diversity to regulate intra-ensemble variability. Experiments on four subjective text-classification benchmarks (ArMIS, ConvAbuse, HS-Brexit, MD-Agreement) show that EDO substantially improves probabilistic calibration, reducing cross-entropy (40–78% depending on baseline) and lowering Brier scores relative to Soft-CE, Soft-MD, Top-5 Voting, and WEL, while maintaining competitive F1 and better alignment with annotator distributions. These results demonstrate that jointly optimizing ensemble structure with a signed diversity regularizer provides an efficient, model-agnostic approach for modeling human subjectivity in supervised learning.' volume: 337 URL: https://proceedings.mlr.press/v337/cui26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/cui26a/cui26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-cui26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xia family: Cui - given: Ziyi family: Huang - given: Nishanthi Rupika family: Abeynayake editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1357-1377 id: cui26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1357 lastpage: 1377 published: 2026-08-06 00:00:00 +0000 - title: 'Communication-Efficient Distributed Training for Collaborative Flat Optima Recovery in Deep Learning' abstract: 'We study centralized distributed data parallel training of deep neural networks (DNNs), aiming to improve the trade-off between communication efficiency and model performance of local gradient methods. Motivated by the flat-minima hypothesis, we first introduce a simple sharpness measure, Inverse Mean Valley, and show it strongly correlates with the generalization gap of DNNs. We then incorporate an efficient relaxation of this measure into the distributed objective as a lightweight regularizer that encourages workers to seek wide minima collaboratively. The regularizer exerts a pushing force that counteracts the consensus step pulling the workers together, giving rise to the Distributed Pull-Push Force ({DPPF}) algorithm. Empirically, {DPPF} generalizes better than other local gradient methods and synchronous gradient averaging while maintaining communication efficiency. In addition, our loss landscape visualizations confirm the ability of {DPPF} to locate flatter minima. Theoretically, we show that {DPPF} drives workers to span flat valleys with valley width governed by push–pull strengths, it yields self-stabilizing dynamics, it obeys generalization guarantees that depend on valley width, and it converges in the non-convex setting.' volume: 337 URL: https://proceedings.mlr.press/v337/dimlioglu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/dimlioglu26a/dimlioglu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-dimlioglu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tolga family: Dimlioglu - given: Anna Ewa family: Choromanska editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1378-1422 id: dimlioglu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1378 lastpage: 1422 published: 2026-08-06 00:00:00 +0000 - title: 'Sparse Action-Dependent Policy Iteration under Coordination Structures: Convergence and Optimality' abstract: 'Action-dependent policies, which condition decisions of each agent on both states and other agents’ actions, provide a powerful structured framework for cooperative multi-agent reinforcement learning ({MARL}). Most existing studies have focused on auto-regressive formulations, where each agent’s policy depends on the actions of all preceding agents. However, this structure suffers from severe scalability limitations as the number of agents grows. In contrast, the theoretical foundations of sparse dependency structures remain largely unexplored. To address this gap, we introduce the Action Dependency Graph ({ADG}) to model sparse inter-agent dependencies. We propose a refined equilibrium concept with respect to the {ADG} that is stronger than the {Nash} equilibrium which often traps independent policies. Furthermore, within Coordination Graphs (CG) structured problems, we show that such an equilibrium attains global optimality when the {ADG} satisfies specific CG-induced conditions. To substantiate our theory, we develop a tabular multi-agent policy iteration algorithm that converges to the refined equilibrium exactly as predicted. We further extend our approach to deep {MARL}, confirming that these structural conditions provide a reliable design principle for scalable and optimal coordination.' volume: 337 URL: https://proceedings.mlr.press/v337/ding26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ding26a/ding26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ding26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jianglin family: Ding - given: Jingcheng family: Tang - given: Gangshan family: Jing editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1423-1447 id: ding26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1423 lastpage: 1447 published: 2026-08-06 00:00:00 +0000 - title: 'Neural Diffusion Intensity Models for Point Process Data' abstract: 'Cox processes model overdispersed point process data via a latent stochastic intensity, but both estimation of the nonparametric intensity model and posterior inference over intensity paths are generally intractable, relying on computationally-heavy {MCMC} methods. We introduce Neural Diffusion Intensity Models, a variational inference framework for Cox processes driven by neural stochastic differential equations (SDEs). Our key theoretical result, based on enlargement of filtrations, shows that conditioning on point process observations preserves the diffusion structure of the latent intensity with an explicit drift correction. This provides guidance on how to choose an appropriate variational family so that {ELBO} maximization coincides with maximum likelihood estimation under sufficient model capacity. We provide an amortized encoder architecture that maps variable-length event sequences to posterior intensity paths by simulating the drift-corrected SDE, replacing repeated {MCMC} runs with a single forward SDE simulation. Experiments on synthetic and real-world data demonstrate accurate recovery of latent intensity dynamics and posterior paths, with orders-of-magnitude speedups over {MCMC}-based methods.' volume: 337 URL: https://proceedings.mlr.press/v337/du26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/du26a/du26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-du26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xinlong family: Du - given: Harsha family: Honnappa - given: Vinayak family: Rao editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1448-1473 id: du26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1448 lastpage: 1473 published: 2026-08-06 00:00:00 +0000 - title: 'One Model to Rule Them All: Canonically Gluing Causal Models Along Shared Substructures' abstract: 'Causal {Bayesian} Networks (CBNs) provide a framework for reasoning about interventions, but analyzing complex systems often requires working with multiple overlapping models or hierarchical levels of granularity. We study how to canonically merge separate causal models that share a common substructure or abstract representation. We formalize this problem using category theory. We construct two distinct categories of causal models where morphisms are defined by maps that commute with interventions. Depending on whether these maps are injective or surjective, they represent causal submodels or causal abstractions, respectively. We demonstrate that the canonical merging of models sharing a common subsystem corresponds to computing a pushout in the category of submodels, while merging models sharing a common abstraction corresponds to a pullback in the category of abstractions. We establish sufficient topological and domain-level conditions under which these universal constructions exist.' volume: 337 URL: https://proceedings.mlr.press/v337/englberger26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/englberger26a/englberger26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-englberger26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Markus family: Englberger - given: Devendra Singh family: Dhami editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1474-1497 id: englberger26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1474 lastpage: 1497 published: 2026-08-06 00:00:00 +0000 - title: 'How PC-based Methods Err: Towards Better Reporting of Assumption Violations and Small Sample Errors' abstract: 'Causal discovery methods based on the {PC} algorithm are proven to be sound if all structural assumptions are fulfilled and all conditional independence tests are correct. This idealized setting is rarely given in real data. In this work, we first showcase how local errors can lead to untrustworthy edge orientations far away from the error source, highlighting how consequential seemingly innocuous errors can become. Next, we introduce coherency scores to find assumption violations and small sample errors in the absence of a ground truth. These scores do not require statistical tests beyond those already executed by the causal discovery algorithm. Errors detected by our approach extend the set of errors that present themselves as orientation conflicts or ambiguities. We place our computationally cheap global error detection and quantification scores as a bridge between computationally expensive global answer-set-programming-based methods and less expensive local error detection methods. The scores are analyzed on simulated and real-world datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/faltenbacher26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/faltenbacher26a/faltenbacher26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-faltenbacher26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sofia family: Faltenbacher - given: Jonas family: Wahl - given: Rebecca Jean family: Herman - given: Jakob family: Runge editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1498-1519 id: faltenbacher26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1498 lastpage: 1519 published: 2026-08-06 00:00:00 +0000 - title: 'Poisson–Gamma Modeling of Inter-Relational Dependencies in Dynamic Knowledge Graphs' abstract: 'Dynamic knowledge graphs are ubiquitous in today’s {AI} applications, as we represent molecular structures, social relationships, and language information using these graph models. As knowledge graphs evolve over time and are often noisy and incomplete, modeling their temporal and relational dependencies becomes crucial for downstream tasks. To address these challenges, this paper proposes PGRE ({Poisson}–Gamma Relational Evolution), a probabilistic model for modeling inter-relational dependencies in dynamic knowledge graphs. PGRE represents multi-relational temporal links via a {Poisson}–{Bernoulli} formulation. It introduces Gamma-distributed latent variables to capture entity–factor associations and cross-relation dependencies mediated by shared latent communities. A Gamma {Markov} process further models the temporal evolution of these latent variables, enabling principled characterization of relational dynamics. Experiments on benchmark datasets show that PGRE achieves competitive performance in link prediction, particularly in sparse settings, while revealing meaningful relational evolution patterns in dynamic knowledge graphs.' volume: 337 URL: https://proceedings.mlr.press/v337/fang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/fang26a/fang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-fang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nan family: Fang - given: Yijun family: Wang - given: Hao family: Liao - given: Sikun family: Yang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1520-1539 id: fang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1520 lastpage: 1539 published: 2026-08-06 00:00:00 +0000 - title: 'Mitigating Spurious Correlations with Memorization-Guided Dataset De-Biasing' abstract: 'Real-world datasets often contain spurious correlations that are not causally related to the target label. When such correlations dominate the majority of training samples, models tend to rely on them, leading to misclassification of minority samples that do not exhibit the same spurious patterns. While a potential approach is to select judicious subsets of data to better represent of the minority samples, it may require group labels which are typically unknown. Furthermore, as we demonstrate, widely used sample scoring functions in the invariant subset or coreset selection literature largely depend on spurious features and therefore fail to accurately capture the importance or difficulty of core, causally relevant features. Accordingly, we propose to mitigate spurious correlations, by developing a two-stage sample scoring function that disentangles the learning dynamics of core and spurious features and evaluates their difficulty separately. Based on our proposed metric, we introduce a new algorithm to find and prioritize informative samples both with and without spurious correlations. Extensive experiments demonstrate that a standard {ERM} model trained on our selected samples achieves superior performance compared to state-of-the-art debiasing techniques, while requiring as little as 10% of the original training data.' volume: 337 URL: https://proceedings.mlr.press/v337/fazla26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/fazla26a/fazla26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-fazla26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Arda family: Fazla - given: Abolfazl family: Hashemi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1540-1573 id: fazla26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1540 lastpage: 1573 published: 2026-08-06 00:00:00 +0000 - title: 'Average Controlled and Average Natural Micro Direct Effects in Summary Causal Graphs' abstract: 'In this paper, we investigate the identifiability of average controlled direct effects and average natural direct effects in causal systems represented by summary causal graphs, which are abstractions of full causal graphs, often used in dynamic systems where cycles and omitted temporal information complicate causal inference. Unlike in the traditional linear setting, where direct effects are typically easier to identify and estimate, non-parametric direct effects, which are crucial for handling real-world complexities, particularly in epidemiological contexts where relationships between variables (e.g., genetic, environmental, and behavioral factors) are often non-linear, are much harder to define and identify. In particular, we give sufficient conditions for identifying average controlled micro direct effect and average natural micro direct effect from summary causal graphs in the presence of hidden confounding. Furthermore, we show that the conditions given for the average controlled micro direct effect become also necessary in the setting where there is no hidden confounding and where we are only interested in identifiability by adjustment.' volume: 337 URL: https://proceedings.mlr.press/v337/ferreira26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ferreira26a/ferreira26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ferreira26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Simon family: Ferreira - given: Charles K. family: Assaad editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1574-1584 id: ferreira26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1574 lastpage: 1584 published: 2026-08-06 00:00:00 +0000 - title: 'Explainable Clustering of Mixture Models' abstract: 'The explainable clustering problem was first posed by Moshkovitz et al. (ICML 2020) and studies how well an axis-aligned decision tree with $K$ leaves can approximate a given clustering. The performance of the tree is measured via the \textit{price of explainability}, defined as the ratio between the clustering cost of the tree (where every leaf is a cluster) and the optimal cost. Several recent works have given worst-case characterizations of the price of explainability for different cost functions. However, these guarantees are data-agnostic and therefore notoriously pessimistic in practical clustering settings. In this paper, we study explainable clustering from the point of view of mixture models, which allows us to give the first data-dependent bounds on the price of explainability. First, we focus on $K$-medians clustering of mixture models with subexponential tails. We propose an algorithm that leverages information about the distribution of the data to find better cuts, and prove new upper and lower bounds. Second, we extend our algorithm and the theoretical guarantees it provides to kernel clustering, thereby refining the existing worst-case analysis.' volume: 337 URL: https://proceedings.mlr.press/v337/fleissner26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/fleissner26a/fleissner26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-fleissner26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Maximilian family: Fleissner - given: Maedeh family: Zarvandi - given: Debarghya family: Ghoshdastidar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1585-1603 id: fleissner26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1585 lastpage: 1603 published: 2026-08-06 00:00:00 +0000 - title: 'Bregman contrastive estimation as a general framework for learning unnormalized models: Efficiency, robustness and optimal noise' abstract: 'Learning unnormalized models is an ubiquitous problem in modern statistics and machine learning. Noise contrastive estimation (NCE) takes a popular approach based on solving a binary classification problem: Unnormalized models are learned by discriminating input data with artificially generated noise data. This paper follows this approach, but proposes a general framework based on the {Bregman} divergence. By selecting the convex function in the divergence, our framework includes existing methods as special cases, and novel variants of NCE can be also derived. Learning unnormalized models in the proposed framework is performed by estimating the posterior probability in the binary classification, i.e., the composition of the logistic function and the ratio of data and noise distributions. Due to the boundedness of the logistic function, our framework is advantageous in outlier-robustness. In fact, we theoretically prove that robust estimation is possible in our framework under a variety of convex functions in the {Bregman} divergence. Furthermore, the asymptotic efficiency is also investigated, implying a trade-off between efficiency and robustness in our framework. Inspired by these results, we derive the optimal noise distribution under some constraints for robustness. Finally, we numerically demonstrate the robustness of the novel variants of NCE and the derived optimal noise distribution.' volume: 337 URL: https://proceedings.mlr.press/v337/fujii26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/fujii26a/fujii26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-fujii26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuto family: Fujii - given: Hiroaki family: Sasaki - given: Takafumi family: Kanamori editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1604-1627 id: fujii26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1604 lastpage: 1627 published: 2026-08-06 00:00:00 +0000 - title: 'Perfect Matching Map Recovery Under Unknown Scalar Affine Transformation' abstract: 'We study the problem of matching two sets of noisy feature vectors when underlying true features are related by an unknown scalar affine transformation. Our method comprises two primary steps. First, we standardize the feature vectors to estimate the unknown scalar affine transformation. Subsequently, we estimate the permutation by minimizing the Least Sum of Logarithms (LSL) between two sets of observations using the estimated transformation. Our main result shows that the unknown permutation can be perfectly recovered given that the minimal separation distance of true feature vectors scales as $\sqrt{\rho_\sigma} \vee (d\log n)^{1/4} \vee \sqrt{\log n}$, where $d$ is the ambient dimension, $n$ is the sample size, and $\rho_\sigma$ is the maximal ratio of noise magnitudes. Interestingly, the obtained rate, under mild heteroscedasticity, coincides with that of the non-affine setting. We additionally demonstrate that there exist configurations requiring a larger minimal separation distance for perfect recovery. The latter makes the matching problem more challenging from minimax perspective compared to the non-affine setting. Consequently, we show that in the problem of feature matching, standardizing the data implicitly estimates the scalar affine parameters. As part of our analysis, we prove non-asymptotic concentration bounds for the affine parameter estimators in the presence of heterogeneous noise magnitudes.' volume: 337 URL: https://proceedings.mlr.press/v337/galstyan26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/galstyan26a/galstyan26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-galstyan26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tigran family: Galstyan - given: Avetik family: Karagulyan - given: Arshak family: Minasyan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1628-1649 id: galstyan26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1628 lastpage: 1649 published: 2026-08-06 00:00:00 +0000 - title: 'Advances in PAC-Bayesian certification of deep neural networks: tighter closed-form inequalities and optimization of bounds on non-differentiable losses' abstract: 'This paper presents three theoretical contributions that improve the usability of risk certificates for neural networks based on {PAC-Bayes} bounds. First, two bounds on the KL divergence between {Bernoulli} distributions enable the derivation of the tightest explicit bounds on the true risk of classifiers across different ranges of empirical risk. Then, a novel method to optimize bounds on non-differentiable objectives is introduced, allowing to optimize risk bounds directly on the 0-1 loss instead of resourcing to a surrogate differentiable loss, such as the bounded cross-entropy. These theoretical contributions are illustrated with an empirical evaluation on the {MNIST} and {CIFAR-10} datasets. In fact, this paper presents the first non data-dependent generalization bounds on the 0-1 loss for neural networks fitted on {CIFAR-10}.' volume: 337 URL: https://proceedings.mlr.press/v337/garcia-perez26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/garcia-perez26a/garcia-perez26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-garcia-perez26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Diego family: García-Pérez - given: Emilio family: Parrado-Hernandez - given: John family: Shawe-Taylor editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1650-1662 id: garcia-perez26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1650 lastpage: 1662 published: 2026-08-06 00:00:00 +0000 - title: 'Conformal Online Model Aggregation' abstract: 'Conformal prediction equips machine learning models with a reasonable notion of uncertainty quantification under mild assumptions. However, conformal prediction only works if we fix the underlying model in advance. A relatively unaddressed issue in conformal prediction is that of model selection and/or aggregation: given a set of prediction models, which one should we conformalize? We suggest that instead of performing model selection, it can be prudent and practical to perform conformal set aggregation in an online, adaptive fashion. We propose a wrapper that takes in several conformal prediction sets, and outputs a single adaptively-combined prediction set. Our method, called conformal online model aggregation ({COMA}), is based on combining the prediction sets from several algorithms by weighted voting, and can be thought of as a sort of online stacking of the underlying conformal sets. As long as the input sets have (distribution-free) coverage guarantees, {COMA} retains coverage guarantees, under a negative correlation assumption between errors and weights. {COMA} is well suited to decentralized settings, where users are only willing to share their prediction sets for a new test point in a black-box fashion. As we demonstrate, it is also well suited to settings with distribution drift, where model selection is not advisable.' volume: 337 URL: https://proceedings.mlr.press/v337/gasparin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/gasparin26a/gasparin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-gasparin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Matteo family: Gasparin - given: Aaditya family: Ramdas editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1663-1683 id: gasparin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1663 lastpage: 1683 published: 2026-08-06 00:00:00 +0000 - title: 'Implicit Learning for Reasoning in First-Order Probabilistic Logic' abstract: 'Reasoning under uncertainty is a fundamental challenge, particularly when inference involves complex computations over large relational domains. Existing probabilistic inference methods typically answer probabilistic queries by leveraging symmetries to perform efficient, lifted inference assuming access to a complete model. However, the upstream task of learning such a model from partial and noisy observations is generally intractable. We propose the first polynomial-time framework for “implicit learning to reason" in a first-order relational probability logic, even over infinite domains. Our approach combines statistical signals from data with semidefinite relaxations of the moment problem, jointly informed by new observations and prior knowledge from the knowledge base. This enables verifying or refuting first-order queries without ever constructing an explicit model. We establish soundness and completeness guarantees for our algorithm, as well as a tractability result.' volume: 337 URL: https://proceedings.mlr.press/v337/ge26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ge26a/ge26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ge26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Luise family: Ge - given: Brendan family: Juba - given: Kris family: Nilsson - given: Alison family: Shao editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1684-1694 id: ge26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1684 lastpage: 1694 published: 2026-08-06 00:00:00 +0000 - title: 'Fast Best-in-Class Regret for Contextual Bandits' abstract: 'We study the problem of stochastic contextual bandits in the agnostic setting, where the goal is to compete with the best policy in a given class without assuming realizability or imposing model restrictions on losses or rewards. In this work, we propose \textit{Online Pessimistic Policy Learning} and establish the first fast rate for regret relative to the best-in-class policy. Our proposed algorithm updates the policy at every round by minimizing a pessimistic objective, defined as a clipped inverse-propensity estimate of the policy value plus a variance penalty. By leveraging entropy assumptions on the policy class and a Hölderian error-bound condition (a generalization of the margin condition), we achieve fast best-in-class regret rates, including polylogarithmic rates in the parametric case. Our analysis is driven by a novel sequential self-normalized maximal inequality for bounded martingale empirical processes, which yields uniform variance-adaptive confidence bounds and guarantees pessimism under adaptive data collection.' volume: 337 URL: https://proceedings.mlr.press/v337/girard26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/girard26a/girard26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-girard26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Samuel family: Girard - given: Aurélien family: Bibaut - given: Jill-Jênn family: Vie - given: Arthur family: Gretton - given: Nathan family: Kallus - given: Houssam family: Zenati editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1695-1724 id: girard26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1695 lastpage: 1724 published: 2026-08-06 00:00:00 +0000 - title: 'Quantification of Credal Uncertainty: A Distance-Based Approach' abstract: 'Credal sets, i.e., closed convex sets of probability measures, provide a natural framework to represent aleatoric and epistemic uncertainty in machine learning. Yet how to \emph{quantify} these two types of uncertainty for a given credal set, particularly in multiclass classification, remains underexplored. In this paper, we propose a distance-based approach to quantify total, aleatoric, and epistemic uncertainty for credal sets. Concretely, we introduce a family of such measures within the framework of Integral Probability Metrics (IPMs). The resulting quantities admit clear semantic interpretations, satisfy natural theoretical desiderata, and remain computationally tractable for common choices of IPMs. We instantiate the framework with the total variation distance and obtain simple, efficient uncertainty measures for multiclass classification. In the binary case, this choice recovers established uncertainty measures, for which a principled multiclass generalization has so far been missing. Empirical results confirm practical usefulness, with favorable performance at low computational cost.' volume: 337 URL: https://proceedings.mlr.press/v337/gonzalez-garcia26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/gonzalez-garcia26a/gonzalez-garcia26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-gonzalez-garcia26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xabier family: Gonzalez-Garcia - given: Siu Lun family: Chau - given: Julian family: Rodemann - given: Michele family: Caprio - given: Krikamol family: Muandet - given: Humberto family: Bustince - given: Sebastien family: Destercke - given: Eyke family: Hüllermeier - given: Yusuf family: Sale editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1725-1747 id: gonzalez-garcia26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1725 lastpage: 1747 published: 2026-08-06 00:00:00 +0000 - title: 'Gaussian Graphical Learning via PSD Constraint for Blockwise Missing Multimodal Data' abstract: '{Gaussian} graphical models, estimated via precision matrices, are popular for uncovering underlying conditional dependencies among variables, yet the case of multimodal data with blockwise missing remains unaddressed. We propose a novel method, Direct Sparse Graphical Learning for Multimodal Data ({DSGL}), to handle this issue using only observed data. The {DSGL} consists of two stages: constructing a pilot estimator for the covariance matrix without imputation as an admissible input for {GLASSO}; and estimating the {DSGL} precision matrix via {GLASSO} with repeated cross-validation tuning. We further propose a thresholded variant to address false-positive edges, a common issue in high-dimensional data. We establish theoretical properties for {DSGL} with respect to element-wise deviation and its ability to recover the true graphical structure. In simulations and an Alzheimer’s Disease Neuroimaging Initiative ({ADNI}) application, {DSGL} outperforms imputation-based and other competing approaches, yielding more accurate graph estimation and lower Frobenius-norm error.' volume: 337 URL: https://proceedings.mlr.press/v337/graves26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/graves26a/graves26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-graves26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Joseph L. family: Graves - given: Yufeng family: Liu - given: Elio family: Zhang - given: Seong-Tae family: Kim - given: family: for the Alzheimer’s Disease Neuroimaging Initiative editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1748-1768 id: graves26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1748 lastpage: 1768 published: 2026-08-06 00:00:00 +0000 - title: 'Eigenvalue Calibration for Semantic Embeddings of Large Language Models' abstract: 'Uncertainty quantification is central to the reliable deployment of large language models ({LLMs}), and eigenvalues of semantic embeddings have recently emerged as a key tool in state-of-the-art methods. However, conventional calibration results developed for classification probabilities cannot be directly transferred to eigenvalues. We address this gap by proposing a novel framework for calibrating the eigenvalues of semantic embeddings. We interpret {LLMs} combined with semantic embeddings of their generated answers as density matrix predictors, and we propose a novel approach to calibrate density matrix predictors by applying temperature scaling to their eigenvalues. We establish entropy–risk equivalence under calibration, derive a central calibration inequality specific to eigenvalues, and prove that temperature-scaled eigenvalues optimize calibration when minimizing proper score risks. Experiments on a variety of real-world settings show that current {LLMs} are systematically overconfident, and validate our theoretical findings. Together, these results advance the foundations and practice of uncertainty quantification for semantic embeddings.' volume: 337 URL: https://proceedings.mlr.press/v337/gruber26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/gruber26a/gruber26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-gruber26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sebastian G. family: Gruber - given: Nassim family: Walha - given: Francis family: Bach - given: Florian family: Buettner editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1769-1789 id: gruber26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1769 lastpage: 1789 published: 2026-08-06 00:00:00 +0000 - title: 'Detecting Out of Distribution Samples using Class Centered Residual Energy in the Discarded PCA Subspace with Weight Alignment' abstract: 'Principal component analysis ({PCA}) has recently been adopted for out-of-distribution ({OOD}) detection, yet most existing methods focus on dominant, high-variance directions of the feature space. This energy-retaining perspective overlooks a crucial fact: discriminative signals separating in distribution (ID) and {OOD} samples often lie in low variance residual components that are typically discarded. Furthermore, prior {PCA}-based scores rely solely on feature geometry, limiting robustness under distributional shift. In this work, we revisit {PCA} for {OOD} detection from an uncertainty aware perspective. Specifically, we propose a residual-aware {OOD} detection framework that explicitly models the discarded subspace of a shared within-class {PCA} basis. By constructing a residual variation score, we capture deviations that are ignored by the leading principal components. To further enhance reliability, we introduce a complementary classifier-weight alignment score that measures the consistency between the selected class-centered residual and the corresponding classifier weight vector. This dual-signal design enables reliable detection even when {OOD} samples exhibit high energy in the dominant subspaces. Extensive experiments across convolutional and transformer backbones show consistent improvements over strong baselines in AUROC and FPR at 95% TPR. This shows that modeling residual structure and integrating geometric and classifier-aware signals leads to more principled and robust {OOD} detection. The code to reproduce the results is available at https://github.com/sgchr273/CREWA.git' volume: 337 URL: https://proceedings.mlr.press/v337/gul26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/gul26a/gul26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-gul26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shreen family: Gul - given: Mohamed family: Elmahallawy - given: Ardhendu family: Tripathy - given: Sanjay family: Madria editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1790-1803 id: gul26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1790 lastpage: 1803 published: 2026-08-06 00:00:00 +0000 - title: 'The Price of Valid Inference After Causal Discovery' abstract: 'Causal effects estimated by covariate adjustment on a discovered graph have invalid confidence intervals, because the graph-selection step is ignored. We develop a unified selective-inference framework. For constraint-based discovery with latent confounders ({FCI}) under Gaussianity, we prove that the selection event, given the execution trace and signs, is a polyhedron in {Fisher}-z space; along the inference direction it becomes polynomial/rational constraints solving to a union of intervals. Inverting the truncated-{Gaussian} approximate pivot gives exact finite-sample $1-\alpha$ coverage, with known $\sigma^2$, of the adjustment functional $\gamma_1(S^\star)$ when $\{i\}\cup S^\star$ contains the outcome’s {Markov} blanket, and approximate coverage otherwise, with a non-vanishing distortion governed by the variance-ratio excess $\rho^2=\sigma^2_{j|X}/\sigma^2_{j|-j}-1$ (small under sparsity); the $\hat\sigma^2$ plug-in does not remove it. This is the first truncation-set characterization handling latent confounders. Coverage of the structural effect $\beta_{i\to j}$ is asymptotically valid up to the same distortion when the adjustment set is valid (exact when $\rho^2=0$), via high-dimensional {FCI} consistency under $d=o(\sqrt n)$. For unmodified GES, heuristic {Taylor} linearization indicates approximate coverage $1-\alpha-O(d^2/\sqrt n)$ when $n\gg d^4(\log d)^2$. In the nonparametric setting, $\Theta(n^{3/4})$-split discovery incurs width ratio $1+\Theta(n^{-1/4})$ versus a known-graph oracle.' volume: 337 URL: https://proceedings.mlr.press/v337/guo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/guo26a/guo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-guo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Dongxin family: Guo - given: Jikun family: Wu - given: Siu Ming family: Yiu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1804-1822 id: guo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1804 lastpage: 1822 published: 2026-08-06 00:00:00 +0000 - title: 'Provably Efficient Reinforcement Learning in Continuous-Time Episodic MDPs with Poisson Decision Epochs' abstract: 'Many real-world reinforcement learning ({RL}) problems evolve in continuous time, where decisions occur at irregular, event-driven intervals rather than at fixed discrete steps. We study episodic continuous-time {Markov} Decision Processes ({MDPs}) in which decision epochs are governed by a homogeneous {Poisson} process and the reward and transition dynamics vary smoothly over time. We consider both a fixed number of jumps per episode and a fixed time budget with a random number of {Poisson} decision epochs. Under a Lipschitz continuity assumption in time, we exploit local smoothness through discretization and extend both UCRL \cite{auer2006logarithmic} and Q-learning \cite{jin2018q} to this setting, proving $\tilde{\mathcal{O}}(T^{2/3})$ regret bounds for both model-based and model-free algorithms. Finally, we establish matching $\tilde{\Omega}(T^{2/3})$ minimax lower bounds, showing that the rate is optimal up to logarithmic factors. These results provide the first tight regret guarantees for Lipschitz-smooth continuous-time episodic {MDPs} with {Poisson} decision epochs.' volume: 337 URL: https://proceedings.mlr.press/v337/guo26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/guo26b/guo26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-guo26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kenny family: Guo - given: Valentio family: Iverson - given: Sahan family: Wijetunga - given: William family: Chang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1823-1856 id: guo26b issued: date-parts: - 2026 - 8 - 6 firstpage: 1823 lastpage: 1856 published: 2026-08-06 00:00:00 +0000 - title: 'Proximal Identification and Estimation in Front-Door Causal Structures with Unobserved Confounding of the Mediator' abstract: 'Unobserved confounding is a fundamental obstacle in causal inference problems. In the graphical modeling literature, a general theory has been developed that allows identification in the presence of hidden variables, with some limitations. In particular, {Pearl}’s celebrated front-door criterion allows nonparametric identification in the presence of unobserved common causes of the treatment and the outcome, however it requires the presence of an unconfounded variable that mediates all causal influence from the treatment to the outcome. This stringent requirement limits the applicability of the front-door criterion. We propose proximal generalizations of the front-door criterion, allowing both arbitrary treatment/outcome confounding, and unobserved confounders of the mediator, provided informative proxies for the latter type of confounders are observed. In addition to deriving three new identification strategies in this setting, we provide plug-in and influence function-based estimation strategies for the resulting functionals, and evaluate their performance through simulations.' volume: 337 URL: https://proceedings.mlr.press/v337/guo26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/guo26c/guo26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-guo26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Helen family: Guo - given: Beatrix Yaxin family: Wen - given: Ilya family: Shpitser editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1857-1881 id: guo26c issued: date-parts: - 2026 - 8 - 6 firstpage: 1857 lastpage: 1881 published: 2026-08-06 00:00:00 +0000 - title: 'Reliable Conformal Prediction for Ordinal Classification Using the Ranked Probability Score' abstract: 'Ordinal classification (OC) arises in high-stakes domains such as medicine and finance, where uncertainty quantification must account for the severity of ordinal errors. Conformal prediction ({CP}) provides distribution-free prediction sets with marginal coverage guarantees; however, its practical effectiveness depends critically on the choice of nonconformity function. We introduce a {CP} method for ordinal classification based on the ranked probability score ({RPS}), a proper scoring rule defined over cumulative predictive distributions. Although it reflects ordinal risk quite naturally, it has largely been neglected in conformal ordinal prediction (COP). When used as a measure of nonconformity, {RPS} yields median-centered contiguous prediction sets by construction. The method is model-agnostic, supports both assessed and grouped ordered categorical outcomes, and permits efficient implementation compared to greedy interval selection procedures. Across multiple ordinal image and tabular datasets, {RPS}-based {CP} produces contiguous prediction sets and strikes a favorable balance between prediction set width and the magnitude of ordinal miscoverage relative to existing {CP} methods.' volume: 337 URL: https://proceedings.mlr.press/v337/haas26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/haas26a/haas26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-haas26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Stefan family: Haas - given: Luca family: Killmaier - given: Alireza family: Javanmardi - given: Eyke family: Hüllermeier editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1882-1912 id: haas26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1882 lastpage: 1912 published: 2026-08-06 00:00:00 +0000 - title: 'A Probabilistic Circuit Framework for Interpretable Graph PU Learning' abstract: 'How can we make graph positive-unlabeled ({PU}) learning interpretable? Existing methods jointly process node features and edge information, which obscures their interaction and makes predictions difficult to interpret. In this paper, we propose a novel interpretable graph {PU} learning framework that explicitly decouples feature and edge processing, enabling multi-level interpretability. Our framework first produces a core prediction from node features using probabilistic circuits (PCs) and then refines it using edge information, providing graph-level interpretability by exposing how graph structure affects predictions. For feature-based prediction, we construct two PCs through a careful split of the training nodes, yielding node-level interpretability by highlighting which nodes support the separation of positive and negative instances. Finally, by leveraging the tractability of PCs, we obtain feature-level interpretability via feature attribute marginalization, which quantifies attribute impact and importance while revealing interactions and dependencies. Experiments on 10 datasets show that our framework achieves strong performance while substantially improving interpretability. The code is available at https://github.com/hagad1/graphpu-cpu.' volume: 337 URL: https://proceedings.mlr.press/v337/hamid26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hamid26a/hamid26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hamid26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sagad family: Hamid - given: Dooho family: Lee - given: Myeong family: Kong - given: Tanya family: Braun - given: Jaemin family: Yoo editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1913-1930 id: hamid26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1913 lastpage: 1930 published: 2026-08-06 00:00:00 +0000 - title: 'Scalable Model-Assisted Multi-Target Estimation in Large Image Collections' abstract: 'Computer vision models are increasingly used as measurement tools to estimate population-level quantities from large image collections, but prediction errors introduce bias and the resulting estimates lack statistical guarantees required in scientific applications. Prior work uses a Monte Carlo framework to combine model predictions with ground-truth annotations by sampling some images for humans to label and is able to provide unbiased estimates with controllable accuracy, but primarily addresses single-scalar estimation. We study the more general problem of multi-target estimation, where many quantities (e.g., class counts or proportions) must be estimated simultaneously, and adapt sampling and estimation strategies from survey sampling to this setting. Evaluations on five detection and segmentation datasets with 7–80 classes show that importance sampling excels with moderate annotation budgets or fewer targets, whereas uniform sampling with control variates is superior when estimating many targets or operating with minimal labels. Additionally, a subset-based ratio estimator remains highly competitive across all regimes. Ultimately, our framework effectively combines biased model predictions and limited human labels into rigorous scientific measurements.' volume: 337 URL: https://proceedings.mlr.press/v337/hamilton26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hamilton26a/hamilton26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hamilton26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Max family: Hamilton - given: Jinlin family: Lai - given: Daniel family: Sheldon - given: Subhransu family: Maji editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1931-1946 id: hamilton26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1931 lastpage: 1946 published: 2026-08-06 00:00:00 +0000 - title: 'Provable Subspace Identification of Nonlinear Multi-view CCA' abstract: 'We investigate the identifiability of nonlinear canonical correlation analysis ({CCA}) in a multi-view setup, in which each view is generated by applying an unknown nonlinear map to a linear mixture of shared latent variables plus view-private noise. Rather than pursuing exact unmixing, which is known to be ill-posed under general nonlinear mixing, we instead reframe multi-view {CCA} as a basis-invariant subspace identification problem. Under suitable latent priors and spectral separation conditions, we prove that the pairwise population {CCA} objective recovers correlated signal subspaces up to view-wise orthogonal ambiguity. For $N \geq 3$ views, their multi-view aggregation provably isolates the jointly correlated subspaces shared across all views while eliminating view-private variation. We further establish finite-sample statistical consistency guarantees by translating the concentration of empirical cross-covariances into explicit subspace error bounds via spectral perturbation theory. Experiments on synthetic and rendered image datasets support our theoretical findings and illustrate the necessity of the assumed conditions.' volume: 337 URL: https://proceedings.mlr.press/v337/han26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/han26a/han26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-han26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhiwei family: Han - given: Stefan family: Matthes - given: Hao family: Shen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1947-1982 id: han26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1947 lastpage: 1982 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Bayesian Decision Making under Adversarial Uncertainty' abstract: 'Scientific experiments are often designed to maximize information gain, yet in many applications the primary objective is to support reliable downstream decision-making. Existing decision-aware experimental design and active learning methods typically assume well-specified outcome models and implicitly rely on the stability of the optimal decision under real-world perturbations. In practice, however, experimental outcomes are frequently influenced by hidden or weakly modeled effects, which can substantially alter decision optimality and lead to misleading conclusions. We study sequential adversarially robust decision-aware experimental design, where data acquisition has to take into account information gain against plausible worst-case unexpected effects, modeled here as variation in adversarial variables. Building on {Bayesian} decision theory, we formalize an adversarially robust optimal decision under this setting and derive a principled {Bayesian} experimental design criterion. The criterion explicitly targets decision stability rather than nominal optimality. Experiments on synthetic and real-world scientific datasets show that conventional decision-aware design can converge rapidly to high confidence yet fragile decisions, while our robustness-aware approach yields decisions that are significantly more stable and reliable under adversarial variation.' volume: 337 URL: https://proceedings.mlr.press/v337/harikumar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/harikumar26a/harikumar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-harikumar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Haripriya family: Harikumar - given: Sammie family: Katt - given: Yasir Zubayr family: Barlas - given: Samuel family: Kaski editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 1983-2007 id: harikumar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 1983 lastpage: 2007 published: 2026-08-06 00:00:00 +0000 - title: 'Should You Use Your Large Language Model to Explore or Exploit?' abstract: 'We evaluate the ability of the current generation of large language models ({LLMs}) to help a decision-making agent facing an exploration-exploitation tradeoff. While previous work has largely study the ability of {LLMs} to solve combined exploration-exploitation tasks, we take a more systematic approach and use {LLMs} to explore and exploit in silos in various (contextual) bandit tasks. We find that reasoning models show the most promise for solving exploitation tasks, although they are still too expensive or too slow to be used in many practical settings. Motivated by this, we study tool use and in-context summarization using non-reasoning models. We find that these mitigations may be used to substantially improve performance on medium-difficulty tasks, however even then, all {LLMs} we study perform worse than a simple linear regression, even in non-linear settings. On the other hand, we find that {LLMs} do help at exploring large action spaces with inherent semantics, by suggesting suitable candidates to explore.' volume: 337 URL: https://proceedings.mlr.press/v337/harris26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/harris26a/harris26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-harris26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Keegan family: Harris - given: Aleksandrs family: Slivkins editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2008-2058 id: harris26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2008 lastpage: 2058 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Bayesian and Markov Networks with an Unreliable Oracle' abstract: 'We study constraint-based structure learning of {Markov} networks and {Bayesian} networks in the presence of an unreliable conditional independence oracle that makes at most a bounded number of errors. For {Markov} networks, we observe that a low maximum number of vertex-wise disjoint paths implies that the structure is uniquely identifiable even if the number of errors is (moderately) exponential in the number of vertices. For {Bayesian} networks, however, we prove that one cannot tolerate any errors to always identify the structure even when many commonly used graph parameters like treewidth are bounded. Finally, we give algorithms for structure learning when the structure is uniquely identifiable.' volume: 337 URL: https://proceedings.mlr.press/v337/harviainen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/harviainen26a/harviainen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-harviainen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Juha family: Harviainen - given: Pekka family: Parviainen - given: Vidya Sagar family: Sharma editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2059-2074 id: harviainen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2059 lastpage: 2074 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Max-Stable Representations that Extrapolate' abstract: 'High-dimensional images and measurements may indicate extreme and rare behavior, such as advanced stages of cancer or material failure, and understanding these distributions is important for many disciplines. Classically, extreme value theory (EVT) provides a theoretical framework for extrapolating based on extremeness of magnitude of measurements and is used to model the tail of a distribution from limited observations. We propose a framework for learning representations from high dimensional observations that are amenable to analysis using classical EVT. Specifically, we propose extending the $\max$-stability property of EVT to $\varphi$-stability, which generalizes the $\max$ operator to a more general operator $\varphi$ that has practical applications in high dimensional cases. We base $\varphi$-stability on representation learning techniques such that the resulting representations lend themselves to analysis by EVT and can model high-dimensional observations of extreme characteristics. This enables our method to extrapolate to observations of extreme behavior in the observation domain. We then extend our method to infinite dimensional observations such as time series. Empirical results indicate the utility of using max-stability for representations to extrapolate beyond the training data.' volume: 337 URL: https://proceedings.mlr.press/v337/hasan26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hasan26a/hasan26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hasan26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ali family: Hasan - given: Patrick Kendal family: Kuiper - given: Yuting family: Ng - given: Jose family: Blanchet - given: Vahid family: Tarokh editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2075-2084 id: hasan26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2075 lastpage: 2084 published: 2026-08-06 00:00:00 +0000 - title: 'Identification and Bounding of Central Moments of Causal Effects Using Marginal Moments Information' abstract: 'Evaluating the causal effect of a treatment on an outcome is a central objective in causal inference. While the average causal effect summarizes the mean impact of treatment, the central moments of the individual causal effect (ICE) characterize the shape of the ICE distribution, thereby revealing the extent and structure of treatment effect heterogeneity across individuals. This paper investigates the identification and bounding of the central moments of the ICE using only the marginal central moments of each potential outcome (PO). Compared with existing approaches that require knowledge of the full marginal distributions of the POs, marginal moment information is often substantially easier to obtain in empirical applications. Finally, we illustrate the practical relevance of our results through two empirical case studies.' volume: 337 URL: https://proceedings.mlr.press/v337/hashimoto26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hashimoto26a/hashimoto26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hashimoto26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Naoya family: Hashimoto - given: Yuta family: Kawakami - given: Jin family: Tian editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2085-2118 id: hashimoto26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2085 lastpage: 2118 published: 2026-08-06 00:00:00 +0000 - title: 'Identifying Labeling Mechanism in Positive–Unlabeled Learning under Unknown Class Prior' abstract: 'Positive–Unlabeled ({PU}) learning critically depends on assumptions about how positive instances are labeled, yet the labeling mechanism is typically unknown in practice. Misspecification of the labeling mechanism can therefore lead to systematic bias and unstable learning. We formulate labeling mechanism identification as a statistical inference problem under an unknown class prior using only positive and unlabeled data. We propose a two-stage testing framework that first constructs a family of empirical positive sets through false discovery rate ({FDR})-controlled multiple testing at multiple {FDR} levels, and then performs bootstrap-based selected completely at random ({SCAR}) consistency tests on each empirical positive set, whose evidence is aggregated via a Bonferroni correction to produce a global decision.We establish that each empirical positive set admits provably controlled contamination, and further show that the Bonferroni-aggregated bootstrap test provides valid inference. Experiments on synthetic and real-world datasets demonstrate that the proposed framework reliably distinguishes {SCAR} from selected at random (SAR) mechanisms and improves the robustness of downstream {PU} learning.' volume: 337 URL: https://proceedings.mlr.press/v337/he26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/he26a/he26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-he26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Siying family: He - given: Weijuan family: Liang - given: Jiatong family: Liu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2119-2136 id: he26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2119 lastpage: 2136 published: 2026-08-06 00:00:00 +0000 - title: 'EpiRDN: A Learnable Anisotropic Reaction-Diffusion Network for Epidemic Time Series Prediction' abstract: 'Epidemic spread on graphs involves local infection dynamics and directional propagation through population movement. Current epidemic graph neural networks combine these aspects using a single symmetric aggregation operator, which limits the learning of their distinct timescales and fails to capture the asymmetry of real epidemic spread. This leads to node representations collapsing to a common state, losing diversity necessary for distinguishing infection stages. To address these issues, we propose EpiRDN, which discretizes the reaction-diffusion equation on graphs and learns its components end-to-end. EpiRDN features a local reaction network for region-level transitions and an anisotropic diffusion operator that utilizes asymmetric attention for directional infection flow. A feature-conditioned damping coefficient balances preserving local identity and neighborhood aggregation. We demonstrate that feature diversity in EpiRDN decays at most geometrically with depth, providing a significant advantage over existing methods. Experiments on four real-world datasets related to influenza and COVID-19 show consistent improvements, especially at longer forecasting horizons.' volume: 337 URL: https://proceedings.mlr.press/v337/hevapathige26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hevapathige26a/hevapathige26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hevapathige26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Asela family: Hevapathige editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2137-2151 id: hevapathige26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2137 lastpage: 2151 published: 2026-08-06 00:00:00 +0000 - title: 'Generalized Distribution-Free Semi-Supervised Learning with Risk Rewrite' abstract: 'Typical semi-supervised learning (SSL) methods rely on distributional assumptions, and their performance degrades when these are violated. While PNU learning, a risk rewriting method, offers a distribution-free alternative, it is restricted to binary classification and its variance optimality remains unclear. In this paper, we propose a generalized framework that constructs unbiased risk estimators using linear combinations of component risks, subsuming PNU learning and extending to multiclass classification. We derive the minimum achievable variance, demonstrating our estimator can attain lower variance than PNU in asymmetric loss scenarios. Furthermore, we establish a generalization bound directly linking this variance reduction to improved learning performance. Based on these theoretical insights, we introduce two practical SSL methods that empirically match or outperform existing approaches on binary and multiclass benchmarks.' volume: 337 URL: https://proceedings.mlr.press/v337/hirose26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hirose26a/hirose26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hirose26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yushi family: Hirose - given: Hiroo family: Irobe - given: Takafumi family: Kanamori editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2152-2178 id: hirose26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2152 lastpage: 2178 published: 2026-08-06 00:00:00 +0000 - title: 'From Bayes’ Rule to Bayes Rules: Information Processing, Bayes’ Theorem, and Imprecise Probabilities' abstract: 'This paper develops principled updating rules for possibilistic inference, where uncertainty about a fixed parameter is represented by a possibility function, the maxitive analogue of a probability distribution, and comparisons are made pointwise via a partial order. From two complementary foundations, an information-conservation viewpoint and an axiomatic viewpoint, we derive the same canonical update: the posterior is the prior-likelihood product followed by supremum normalisation. The two derivations agree for an arbitrary loss, differing only in where the learning-rate parameter enters. This parameter controls epistemic strength and is not identifiable from the normalising evidence alone, clarifying the role of analogous learning-rate parameters in generalised {Bayesian} updating.' volume: 337 URL: https://proceedings.mlr.press/v337/houssineau26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/houssineau26a/houssineau26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-houssineau26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jeremie family: Houssineau - given: Badr-Eddine family: Chérief-Abdellatif editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2179-2195 id: houssineau26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2179 lastpage: 2195 published: 2026-08-06 00:00:00 +0000 - title: 'Policy-Based Trajectory Clustering in Offline Reinforcement Learning' abstract: 'We introduce the task of clustering trajectories in offline reinforcement learning ({RL}) datasets to address the multi-modal nature of offline data. Such datasets often contain trajectories from diverse policies, and treating them as a single distribution can obscure structure and increase distributional shift. We formalize trajectory clustering by linking the KL-divergence of offline trajectory distributions with mixtures of policy-induced distributions. To solve this, we propose Policy-Guided K-means (PG-Kmeans) and Centroid-Attracted Autoencoder (CAAE). PG-Kmeans iteratively trains behavior cloning policies and assigns trajectories based on generation probabilities, while CAAE learns continuous latent representations regularized by a learnable codebook to achieve end-to-end clustering. We prove finite-step convergence of PG-Kmeans and analyze the ambiguity of optimal solutions caused by policy-induced conflicts. Experiments on D4RL and GridWorld show that PG-Kmeans and CAAE partition trajectories into coherent clusters and offer a framework for structuring offline data, with applications in data selection, curriculum learning, and policy transfer.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26a/wang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xinqi family: Wang - given: Simon Shaolei family: Du - given: Hao family: Hu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2196-2222 id: wang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2196 lastpage: 2222 published: 2026-08-06 00:00:00 +0000 - title: 'From Global to Factor-Wise Expert Composition in Discrete Diffusion Models' abstract: 'Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the {ARC-AGI} benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.' volume: 337 URL: https://proceedings.mlr.press/v337/huang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/huang26a/huang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-huang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Haozhe family: Huang - given: Yudong family: Xu - given: Abhijoy family: Mandal - given: Alan family: Aspuru-Guzik editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2223-2243 id: huang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2223 lastpage: 2243 published: 2026-08-06 00:00:00 +0000 - title: 'Model-Agnostic Online Certificate-Driven Calibration for Time Series Forecasting Under Distribution Shift' abstract: 'Time series out-of-distribution generalization requires forecasters to remain reliable when deployment dynamics differ from training conditions due to covariate shift, concept shift, and temporal dependence. Probably Approximately Correct {Bayesian} domain adaptation provides computable certificates by decomposing target risk into a source risk term, a source-to-target mismatch term, and a complexity term, but standard analyses rely on independent sampling and distributional stability, assumptions that are violated in time series by serial dependence and nonstationary shift. We propose a model-agnostic online martingale Probably Approximately Correct {Bayesian} framework that yields finite-sample certificates under temporal dependence and distribution shift. The certificate replaces independent-sample concentration with martingale concentration that adapts to loss scale and predictable variation. We use the certificate as a surrogate regularizer for online calibration by training a gated residual {Bayesian} head on top of a fixed forecasting backbone, producing a corrective update that reverts to the backbone prediction when the gate is closed. Online calibration combines a source risk anchor, a posterior-shift penalty, and a time-adaptive mismatch term computed from target windows observed before forecasting. It follows a predict-then-update protocol in which outcomes become available only after forecasting and are used to update subsequent predictions. Experiments across convolutional, attention-based, and large language model-based forecasters show improved stability and accuracy under covariate and concept shift.' volume: 337 URL: https://proceedings.mlr.press/v337/huang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/huang26b/huang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-huang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Chenfeng family: Huang - given: Zixuan family: Ma - given: George family: Michailidis editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2244-2273 id: huang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 2244 lastpage: 2273 published: 2026-08-06 00:00:00 +0000 - title: 'Balancing Expressivity and Learnability in Quantum Kernel Bandit Optimization' abstract: 'We investigate {Gaussian} Process (GP) bandit optimization utilizing quantum kernels. While quantum kernels enable embedding data into high-dimensional {Hilbert} spaces—potentially offering enhanced expressivity or a "quantum advantage"—this property can pose challenges in bandit learning. Specifically, employing full quantum kernels naïvely may lead to increased model complexity and, consequently, higher cumulative regret impacting the learnability. To address this, we explore the use of projected quantum kernels and classical kernel approximation techniques, which effectively reduce feature dimensionality while preserving essential quantum properties. We demonstrate that these approaches can yield improved regret bounds by strategically balancing approximation error and information gain. Empirical results show that they significantly outperform models based on full quantum kernels in bandit optimization tasks. Additionally, we analyze how to select the optimal model complexity to achieve a favorable trade-off between expressivity and learnability. Our methods also substantially reduce computational costs by simplifying kernel-based inference to linear models, since only a finite set of reduced features is required.' volume: 337 URL: https://proceedings.mlr.press/v337/huang26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/huang26c/huang26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-huang26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuqi family: Huang - given: Vincent Y. F. family: Tan - given: Sharu Theresa family: Jose editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2274-2313 id: huang26c issued: date-parts: - 2026 - 8 - 6 firstpage: 2274 lastpage: 2313 published: 2026-08-06 00:00:00 +0000 - title: 'Probabilistic Edge Modulation for High-Dimensional Causal Discovery' abstract: 'Causal discovery in high-dimensional linear {Bayesian} networks is challenging, even with partial structural knowledge. Such information is often edge-specific and noisy, and naively enforcing uniform shrinkage or hard constraints can induce incorrect or unstable edge selection. We propose Probabilistic Edge Modulation ({PEM}), a principled probabilistic framework that replaces hard structural constraints with soft, edge-specific modulation via a spike-and-slab formulation. {PEM} integrates heterogeneous priors into ordering recovery and parent selection through a unified {MAP} formulation that remains computationally tractable in polynomial time. We establish high-dimensional consistency under both sub-{Gaussian} and heavy-tailed errors with bounded moments, and demonstrate robustness to prior misspecification. Experiments on synthetic and real retail data demonstrate improved structural stability and graph recovery in sparse and data-limited regimes; in a real e-commerce dataset, probabilistic transfer from a data-rich group stabilizes smaller groups and yields nontrivial graphs that do not collapse to near-empty graphs.' volume: 337 URL: https://proceedings.mlr.press/v337/hwang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/hwang26a/hwang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-hwang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Seyong family: Hwang - given: Kyoungjae family: Lee - given: Sunmin family: Oh - given: Gunwoong family: Park editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2314-2335 id: hwang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2314 lastpage: 2335 published: 2026-08-06 00:00:00 +0000 - title: 'Achieving Alignment Through Adaptive Play: Helping Optimize Objectives Without Observing Them' abstract: 'We study problems where two agents seek to minimize an objective that is known only to one of the agents. This setting arises in human-machine and {AI}-{AI} interactions where one agent’s objective is private knowledge inaccessible to the other, referred to as the "helper". We propose a game-theoretic learning algorithm that provably converges to optimal policies through repeated interaction without solving an inverse problem to recover the unknown objective. Importantly, the helper agent has no access to the cost function, its values, or its gradients, and operates under action-only feedback. Despite the information limitation, we establish convergence guarantees under {Polyak-Lojasiewicz} and Lipschitz-gradient assumptions. We validate the approach through two sets of experiments: human-machine interaction and a cart-pole environment with a reinforcement learning agent. In each of these experiments, the helper uses our proposed algorithm. Across scalar and multidimensional action spaces, we demonstrate consistent convergence under action-only feedback.' volume: 337 URL: https://proceedings.mlr.press/v337/isa26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/isa26a/isa26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-isa26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jason T. family: Isa - given: Samuel family: Burden - given: Lillian J. family: Ratliff editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2336-2377 id: isa26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2336 lastpage: 2377 published: 2026-08-06 00:00:00 +0000 - title: 'Byzantine-Robust and Differentially Private Federated Optimization under Weaker Assumptions' abstract: 'Federated Learning (FL) enables heterogeneous clients to collaboratively train a shared model without centralizing their raw data, offering an inherent level of privacy. However, gradients and model updates can still leak sensitive information, while malicious servers may mount adversarial attacks such as Byzantine manipulation. These vulnerabilities highlight the need to address differential privacy ({DP}) and Byzantine robustness within a unified framework. Existing approaches, however, often rely on unrealistic assumptions such as bounded gradients, require auxiliary server-side datasets, or fail to provide convergence guarantees. We address these limitations by proposing Byz-Clip21-SGD2M, a new algorithm that integrates robust aggregation with double momentum and carefully designed clipping. We prove high-probability convergence guarantees under standard $L$-smoothness and $\sigma$-sub-{Gaussian} gradient noise assumptions, thereby relaxing conditions that dominate prior work. Our analysis recovers state-of-the-art convergence rates in the absence of adversaries and improves utility guarantees under Byzantine and {DP} settings. Empirical evaluations on CNN and MLP models trained on {MNIST} further validate the effectiveness of our approach.' volume: 337 URL: https://proceedings.mlr.press/v337/islamov26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/islamov26a/islamov26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-islamov26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Rustem family: Islamov - given: Grigory family: Malinovsky - given: Alexander family: Gaponov - given: Aurelien family: Lucchi - given: Peter family: Richtárik - given: Eduard family: Gorbunov editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2378-2441 id: islamov26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2378 lastpage: 2441 published: 2026-08-06 00:00:00 +0000 - title: 'Graph-Dependent Regret Bounds in Multi-Armed Bandits with Interference' abstract: 'We study multi-armed bandits under network interference, where each unit’s reward depends on its own treatment and those of its neighbors in a given graph. This induces an exponentially large action space, making standard approaches computationally impractical. We propose a novel algorithm that uses the local graph structure to minimize regret. We derive a graph-dependent upper bound on cumulative regret that improves over prior work. Additionally, we provide the first lower bounds for bandits with arbitrary network interference, where each bound involves a distinct structural property of the graph. These bounds show that for both dense and sparse graphs, our algorithm is nearly optimal, with matching upper and lower bounds up to logarithmic factors. When the interference graph is unknown, a variant of our algorithm is Pareto optimal: no algorithm can uniformly outperform it across all instances. We complement our theoretical results with numerical experiments, showing that our approach outperforms the baseline methods.' volume: 337 URL: https://proceedings.mlr.press/v337/jamshidi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/jamshidi26a/jamshidi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-jamshidi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Fateme family: Jamshidi - given: Mohammad family: Shahverdikondori - given: Negar family: Kiyavash editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2442-2460 id: jamshidi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2442 lastpage: 2460 published: 2026-08-06 00:00:00 +0000 - title: 'Optimal Conformal Prediction under Epistemic Uncertainty' abstract: 'Conformal prediction ({CP}) is a widely used frequentist framework to quantify uncertainty by constructing prediction sets with user-specified marginal coverage guarantees. In practice, {CP} is typically applied on top of probabilistic classifiers, which are able to express aleatoric but not epistemic uncertainty. In this paper, we consider the question of how to optimally employ {CP} on top of a more expressive formalism, namely credal sets, which can express both aleatoric and epistemic uncertainty. More specifically, we propose probabilistic {Bernoulli} prediction sets and derive a variant that achieves conditional coverage for valid credal sets while remaining minimal in expected size. We then address the more realistic scenario in which the validity of the credal sets is not guaranteed. Assuming access to calibration data with ground-truth distributions over labels, we apply conformal risk control to BPS and derive a {PAC}-style guarantee: with high probability over the data, the achieved conditional coverage is at least the desired level. We validate our theoretical findings empirically over various datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/javanmardi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/javanmardi26a/javanmardi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-javanmardi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Alireza family: Javanmardi - given: Soroush family: H. Zargarbashi - given: Santo M. A. R. family: Thies - given: Willem family: Waegeman - given: Aleksandar family: Bojchevski - given: Eyke family: Hüllermeier editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2461-2479 id: javanmardi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2461 lastpage: 2479 published: 2026-08-06 00:00:00 +0000 - title: 'Calibration-Aware Online Adaptation under Label Shift' abstract: 'We study online adaptation of a pre-trained base classifier to streaming unlabeled data under label shift, where the marginal label proportions in the stream differ from those in the offline training data. We consider the case where the base classifier’s model class may be misspecified, motivating a separate, calibrated auxiliary classifier used solely to estimate the target label proportions. While many works have studied this setting, it is less understood how calibration quality affects the performance of the adapted base classifier in an online setting. In this paper, we thoroughly analyze the estimation error of the adapted base classifier after the deployment of a novel algorithm that estimates the target label proportions in an online fashion and dynamically adapts the base classifier using the estimated proportions. We decompose the error into a term that vanishes over time and a term determined by calibration quality. Moreover, we characterize an explicit trade-off between calibration granularity and finite-sample calibration error, and propose a novel calibration strategy which effectively balances this trade-off.' volume: 337 URL: https://proceedings.mlr.press/v337/jeong26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/jeong26a/jeong26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-jeong26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jiun family: Jeong - given: Byeongwoo family: An - given: Gi-Soo family: Kim - given: Kyubo family: Shin editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2480-2516 id: jeong26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2480 lastpage: 2516 published: 2026-08-06 00:00:00 +0000 - title: 'Score-Based Diffusion Priors for Adaptive Conformal Inference under Distribution Shift' abstract: 'Conformal prediction provides a distribution-free coverage guarantee for predictive inference, yet its validity degrades under distribution shift, a common challenge in real-world deployment. We introduce {DiffConf}, a framework that uses score-based diffusion models as expressive priors over the data-generating process to enable adaptive conformal inference under temporal and covariate distribution shifts. The main idea is that the score function learned by a diffusion model encodes rich geometric information about the data manifold, which can be repurposed to construct nonconformity scores that are sensitive to distributional changes. We derive a diffusion-guided conformity score that integrates the learned score field with a lightweight online recalibration mechanism, providing finite-sample marginal coverage guarantees even when the data distribution evolves over time. Theoretically, we establish that {DiffConf} achieves asymptotic conditional coverage under mild regularity conditions on the drift rate, and we prove a regret bound that scales gracefully with the complexity of the distribution shift. Experiments on synthetic benchmarks, real-world tabular regression tasks, and high-dimensional image datasets demonstrate that {DiffConf} produces prediction sets that are simultaneously valid and more efficient than existing adaptive conformal methods, reducing average set size by 6–39% across the real-data benchmarks (and by over 50% under large synthetic mean shifts) while keeping coverage within one point of target.' volume: 337 URL: https://proceedings.mlr.press/v337/jiang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/jiang26a/jiang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-jiang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xiangyu family: Jiang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2517-2537 id: jiang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2517 lastpage: 2537 published: 2026-08-06 00:00:00 +0000 - title: 'Improving the Convergence of Private Shuffled Gradient Methods with Public Data' abstract: 'We consider the problem of differentially private ({DP}) convex empirical risk minimization ({ERM}). While the standard {DP}-{SGD} algorithm is theoretically well-established, practical implementations often rely on shuffled gradient methods that traverse the training data sequentially rather than sampling with replacement in each iteration. Despite their widespread use, the theoretical privacy-accuracy trade-offs of private shuffled gradient methods ($\textit{{DP}-ShuffleG}$) remain poorly understood, leading to a gap between theory and practice. In this work, we leverage privacy amplification by iteration (PABI) and a novel application of {Stein}’s lemma to provide the first empirical excess risk bound of $\textit{{DP}-ShuffleG}$. Our result shows that data shuffling results in worse empirical excess risk for $\textit{{DP}-ShuffleG}$ compared to {DP}-{SGD}. To address this limitation, we propose $\textit{Interleaved-ShuffleG}$, a hybrid approach that integrates public data samples in private optimization. By alternating optimization steps that use private and public samples, $\textit{Interleaved-ShuffleG}$ effectively reduces empirical excess risk. Our analysis introduces a new optimization framework with surrogate objectives, varying levels of noise injection, and a dissimilarity metric, which can be of independent interest. Our experiments on diverse datasets and tasks demonstrate the superiority of $\textit{Interleaved-ShuffleG}$ over several baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/jiang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/jiang26b/jiang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-jiang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shuli family: Jiang - given: Pranay family: Sharma - given: Zhiwei Steven family: Wu - given: Gauri family: Joshi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2538-2594 id: jiang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 2538 lastpage: 2594 published: 2026-08-06 00:00:00 +0000 - title: 'PRISM: Calibrated Bayesian Fusion and Auditable Attribution for Reliable LLM Event Prediction from Text' abstract: 'We study event prediction from news text when intermediate drivers are not expert-annotated. Directly prompting large language models ({LLMs}) for forecast probabilities can yield miscalibrated outputs and explanations that are hard to audit. We propose the Probabilistic Reliability and Interpretability System, PRISM, which separates semantic extraction from probabilistic decision making. PRISM uses {LLMs} only to extract interpretable factors, treats repeated extractions as noisy measurements of latent states, and performs {Bayesian} inference to produce posterior predictive probabilities that propagate extraction and measurement uncertainty. For empirical reliability under temporal dependence, we add low-capacity post-hoc calibration and time-adaptive conformal prediction and report calibration and coverage diagnostics. PRISM also reports factor-contrast association summaries with uncertainty and explicit interpretation boundaries. On a {UCDP}–{GDELT} conflict benchmark, PRISM achieves AUROC 0.821 and {ECE} 0.058 on the test set; at 90% target coverage, it attains empirical coverage 0.908 with average set size 1.38.' volume: 337 URL: https://proceedings.mlr.press/v337/jin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/jin26a/jin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-jin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Chengyuan family: Jin - given: Daojian family: Zeng - given: Kang family: Liu - given: Jun family: Zhao - given: Yubo family: Chen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2595-2617 id: jin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2595 lastpage: 2617 published: 2026-08-06 00:00:00 +0000 - title: 'Who Guards the Guardians? The Challenges of Evaluating Identifiability of Learned Representations' abstract: 'Identifiability in representation learning is commonly evaluated using standard metrics (e.g., *MCC, $R^2$, DCI*) on synthetic benchmarks with known ground-truth factors. These metrics are assumed to reflect recovery up to the equivalence class guaranteed by identifiability theory. We show that this assumption holds only under specific structural conditions: each metric implicitly encodes assumptions about both the data-generating process ({DGP}) and the encoder. When these assumptions are violated, metrics become misspecified and can produce systematic false positives and false negatives. Such failures occur both within classical identifiability regimes and in post-hoc settings where identifiability is most needed. We introduce a taxonomy separating {DGP} assumptions from encoder geometry, use it to characterise the validity domains of existing metrics, and release an evaluation suite for reproducible stress testing and comparison.' volume: 337 URL: https://proceedings.mlr.press/v337/joshi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/joshi26a/joshi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-joshi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shruti family: Joshi - given: Théo family: Saulus - given: Wieland family: Brendel - given: Philippe family: Brouillard - given: Dhanya family: Sridhar - given: Patrik family: Reizinger editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2618-2660 id: joshi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2618 lastpage: 2660 published: 2026-08-06 00:00:00 +0000 - title: 'Information-Theoretic Bayesian Optimization for Bilevel Optimization Problems' abstract: 'A bilevel optimization problem consists of two optimization problems nested as an upper- and a lower-level problem, in which the optimality of the lower-level problem defines a constraint for the upper-level problem. This paper considers {Bayesian} optimization (BO) for the case that both the upper- and lower-levels involve expensive black-box functions. Because of its nested structure, bilevel optimization has a complex problem definition, by which bilevel BO has not been widely studied compared with other standard extensions of BO such as multi-objective or constraint problems. We propose an information-theoretic approach that considers the information gain of both the upper- and lower-optimal solutions and values. This enables us to define a unified criterion that measures the benefit for both level problems, simultaneously. Further, we also show a practical lower bound based approach to evaluating the information gain. We empirically demonstrate the effectiveness of our proposed method through several benchmark datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/kanayama26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kanayama26a/kanayama26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kanayama26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Takuya family: Kanayama - given: Yuki family: Ito - given: Tomoyuki family: Tamura - given: Masayuki family: Karasuyama editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2661-2687 id: kanayama26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2661 lastpage: 2687 published: 2026-08-06 00:00:00 +0000 - title: 'Conditional Diffusion Models for Imbalanced Tabular Regression' abstract: 'Imbalanced regression, where certain continuous target ranges are severely underrepresented, poses a fundamental challenge for predictive modeling under uncertainty. Existing oversampling methods rely on local interpolation, which fails to capture complex conditional distributions in rare target regions. We propose TabOversample, a conditional diffusion framework that generates high-fidelity synthetic tabular samples for underrepresented targets via a relevance-weighted denoising objective. We establish four theoretical results: equivalence of relevance weighting to maximum likelihood under a reweighted measure, targeted probability mass amplification in rare regions, quality guarantees for generate-then-filter sampling through order statistics, and a formal connection to distributionally robust optimization over a chi-squared uncertainty set. Across nine benchmark imbalanced regression datasets—four numerical-dominant and five categorical-rich—and against thirteen oversampling and reweighting baselines evaluated over ten seeds, TabOversample attains the best relevance-weighted error (SERA) on eight of nine datasets and the best rare-region RMSE on all nine, substantially improving prediction accuracy in rare target regions while maintaining overall performance.' volume: 337 URL: https://proceedings.mlr.press/v337/kang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kang26a/kang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nathaniel family: Kang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2688-2712 id: kang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2688 lastpage: 2712 published: 2026-08-06 00:00:00 +0000 - title: 'COBALT: Censored Optimization and Bayesian Active Learning Techniques' abstract: 'We target {Bayesian} Active Learning ({AL}) and Optimization (BO) for censored data regimes. While the Tobit likelihood accurately models such clipped observations, its mixed continuous-discrete nature impedes the analytical evaluation of information-theoretic acquisition functions. To address this, we investigate Censored Optimization via {Bayesian} Active Learning Techniques ({COBALT}). We establish rigorous theoretical guarantees for this framework, proving posterior consistency and the asymptotic normality of the {MAP} estimator under greedy maximization. Central to our framework is the derivation of a closed-form entropy for the Censored Normal distribution, enabling an analytical {BALD} ({Bayesian} Active Learning by Disagreement) score compatible with any {Gaussian} posterior approximations. We further underpin this method by deriving a numerically stable Evidence Lower Bound ({ELBO}) for censored atoms, utilizing robust approximations of the log-normal cumulative density. Empirical evaluations using our open-source implementation demonstrate {COBALT}’s best accuracy–compute trade-off among censored-likelihood methods in learning GP posteriors and effectiveness on a variety of benchmarks.' volume: 337 URL: https://proceedings.mlr.press/v337/karlova26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/karlova26a/karlova26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-karlova26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Andrea family: Karlova - given: Rishabh family: Kabra - given: Daniel Augusto prefix: de family: Souza - given: Brooks family: Paige editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2713-2743 id: karlova26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2713 lastpage: 2743 published: 2026-08-06 00:00:00 +0000 - title: 'Likelihood hacking in probabilistic program synthesis' abstract: 'When language models are trained by reinforcement learning ({RL}) to write probabilistic programs, they can artificially inflate their marginal-likelihood reward by producing programs whose data distribution fails to normalise instead of fitting the data better. We call this failure likelihood hacking (LH). We formalise LH in a core probabilistic programming language (PPL) and give sufficient syntactic conditions for its prevention, proving that a safe language fragment $L_{safe}$ satisfying these conditions cannot produce likelihood-hacking programs. Empirically, we show that GRPO-trained models generating PyMC code discover LH exploits within the first few training steps, driving violation rates well above the untrained-model baseline. We implement $L_{safe}$’s conditions as SafeStan, a LH-resistant modification of Stan, and show empirically that it suppresses LH under optimisation pressure. These results show that language-level safety constraints are both theoretically grounded and effective in practice for automated {Bayesian} model discovery.' volume: 337 URL: https://proceedings.mlr.press/v337/karwowski26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/karwowski26a/karwowski26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-karwowski26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jacek family: Karwowski - given: Younesse family: Kaddar - given: Zihuiwen family: Ye - given: Esmeralda S. family: Whitammer - given: Sam family: Staton editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2744-2791 id: karwowski26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2744 lastpage: 2791 published: 2026-08-06 00:00:00 +0000 - title: 'General Bayesian Policy Learning' abstract: 'This study proposes the General {Bayes} framework for policy learning. We consider decision problems in which a decision-maker chooses an action from an action set to maximize its expected welfare. Typical examples include treatment choice and portfolio selection. In such problems, the statistical target is a decision rule, and the prediction of each outcome $Y(a)$ is not necessarily of primary interest. We formulate this policy learning problem by loss-based {Bayesian} updating. Our main technical device is a squared-loss surrogate for welfare maximization. We show that maximizing empirical welfare over a policy class is equivalent to minimizing a scaled squared error in the outcome difference, up to a quadratic regularization controlled by a tuning parameter $\zeta>0$. This rewriting yields a General {Bayes} posterior over decision rules that admits a {Gaussian} pseudo-likelihood interpretation. We clarify two {Bayesian} interpretations of the resulting generalized posterior, a working {Gaussian} view and a decision-theoretic loss-based view. As one implementation example, we introduce neural networks with tanh-squashed outputs. Finally, we provide theoretical guarantees in a {PAC-Bayes} style.' volume: 337 URL: https://proceedings.mlr.press/v337/kato26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kato26a/kato26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kato26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Masahiro family: Kato editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2792-2827 id: kato26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2792 lastpage: 2827 published: 2026-08-06 00:00:00 +0000 - title: 'Stochastic Dominance Driven First-Order Policy Optimization for Multi-Objective Reinforcement Learning' abstract: 'We study multi-objective reinforcement learning with stochastic, vector-valued returns and propose a policy improvement principle based on multivariate $k$th-order stochastic dominance in the lower-orthant sense. Rather than scalarizing objectives or comparing only expected values, we compare entire return distributions using $k$th-order integrated cumulative distribution functions (cdfs). This yields a max-violation objective that measures the worst-case dominance gap of a candidate policy relative to the incumbent policy. Under some regularity assumptions, we show that the Orthant Dominance Policy Optimization (ORDO) algorithm we introduce drives this objective to a point that certifies $\epsilon$-almost non-dominatedness, meaning that no policy in the class can improve the incumbent by more than $\epsilon$. We also propose smoothing approaches for the hinge structure inherent in integrated cdfs, which improve stability and enable stable stochastic gradients in optimization.' volume: 337 URL: https://proceedings.mlr.press/v337/kaya26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kaya26a/kaya26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kaya26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ege Can family: Kaya - given: Kadierdan family: Kaheman - given: Jason M family: Cloud - given: Abolfazl family: Hashemi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2828-2876 id: kaya26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2828 lastpage: 2876 published: 2026-08-06 00:00:00 +0000 - title: 'Joint MDPs and Reinforcement Learning in Coupled-Dynamics Environments' abstract: 'Many distributional quantities in reinforcement learning are intrinsically joint across actions, including distributions of gaps and probabilities of superiority. However, the classical {Markov} decision process ({MDP}) formalism specifies only marginal laws and leaves the joint law of counterfactual one-step outcomes across multiple possible actions at a state unspecified. We study coupled-dynamics environments with a multi-action generative interface which can sample counterfactual one-step outcomes for multiple actions under shared exogenous randomness. We propose joint {MDPs} (JMDPs) as a formalism for such environments by augmenting an {MDP} with a multi-action sample transition model which specifies a coupling of one-step counterfactual outcomes, while preserving standard {MDP} interaction as marginal observations. We adopt and formalize a one-step coupling regime where dependence across actions is confined to immediate counterfactual outcomes at the queried state. In this regime, we derive {Bellman} operators for $n$th-order return moments, providing dynamic programming and incremental algorithms with convergence guarantees.' volume: 337 URL: https://proceedings.mlr.press/v337/kaya26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kaya26b/kaya26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kaya26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ege Can family: Kaya - given: Mahsa family: Ghasemi - given: Abolfazl family: Hashemi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2877-2893 id: kaya26b issued: date-parts: - 2026 - 8 - 6 firstpage: 2877 lastpage: 2893 published: 2026-08-06 00:00:00 +0000 - title: 'Adaptive Cumulative Mass Calibration with Conformal Prediction' abstract: 'Reliable probability estimates by classifiers are essential in high-risk applications. In practice, however, predicted probabilities are often miscalibrated, and many existing post-hoc calibration methods typically lack guarantees that a specific notion of calibration is achieved after the correction procedure is applied. We introduce a *set-based* perspective on calibration through the notion of *cumulative mass calibration* and the corresponding error measures. We propose a new calibration procedure based on conformal prediction that forms cumulative probabilities with guaranteed marginal coverage. We introduce an __adaptive temperature scaling algorithm__, with the temperature tuned for each input to satisfy the conformal coverage constraint. As we show, this procedure can be efficiently implemented. Across image classification tasks, particularly in settings with many classes, our method improves newly introduced calibration error measures (__CMCE__ and $\alpha$__-CMCE__) *and* standard metrics (such as {ECE}, cw-{ECE}, MCE) over the existing baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/kazantsev26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kazantsev26a/kazantsev26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kazantsev26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Daniil family: Kazantsev - given: Eric family: Moulines - given: Maxim family: Panov - given: Nikita family: Kotelevskii - given: Mohsen family: Guizani editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2894-2916 id: kazantsev26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2894 lastpage: 2916 published: 2026-08-06 00:00:00 +0000 - title: 'Conformal Risk Sharing: Certified Cost Allocation with Participation Guarantees' abstract: 'Sharing the financial impact of rare adverse events across a group can soften extreme individual burdens, but any participant made worse off by the arrangement has reason to leave. A credible mechanism must therefore provide each agent with a trustworthy cap on their future obligation and should be deployed only if the aggregate harm across participants is bounded. We formalise this as the Certified Allocation Problem: from finite data and without distributional assumptions, find a redistribution rule, produce obligation caps for every participant, and verify that no participant is made materially worse off. We propose Conformal Risk Sharing, which solves this problem by pairing an interpretable sharing policy with split conformal calibration. The sharing intensity is tuned on training data, while held-out calibration data produces distribution-free per-agent guarantees (valid under exchangeability). Experiments on synthetic and real-world data, including precipitation and energy-cooperative data, confirm that the framework can substantially reduce extreme obligations for high-risk agents while controlling harm to others.' volume: 337 URL: https://proceedings.mlr.press/v337/kazlauskaite26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kazlauskaite26a/kazlauskaite26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kazlauskaite26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ieva family: Kazlauskaite editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2917-2933 id: kazlauskaite26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2917 lastpage: 2933 published: 2026-08-06 00:00:00 +0000 - title: 'Capacity and Redundancy Trade-offs in Multi-Task Learning' abstract: 'In multi-task learning (MTL) negative transfer is often considered as an optimization artifact, but it can also be viewed as a consequence of limited shared capacity and weak task redundancy. We investigate this effect through a Capacity–Redundancy ({CR}) identity that decomposes the sum of per-task predictive informations into joint predictive information that includes label redundancy defined via total correlation, and a residual coupling term that quantifies interference left unresolved by the shared representation. Additionally, we show two key results: (i) a clustering-gap decomposition that gives a necessary and sufficient condition for clustered sharing to outperform global sharing, and (ii) a gradient–TC bridge in a {Gaussian} multi-task model that formally justifies gradient cosine similarity as a proxy for redundancy ordering. Empirically, we estimate $\Delta$ from validation residual correlations, showing that clustered {LoRA} substantially reduces $\widehat{\Delta}$, outperforms size-matched random partitions, and results in statistically significant gains with multi-seed confidence intervals.' volume: 337 URL: https://proceedings.mlr.press/v337/khan26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/khan26a/khan26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-khan26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Asif family: Khan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2934-2957 id: khan26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2934 lastpage: 2957 published: 2026-08-06 00:00:00 +0000 - title: 'Don’t Test What You Can Deduce: Causal Discovery with Logical Inference' abstract: 'Constraint-based causal discovery relies on conditional independence tests (CITs), which are highly unstable in high-dimensional settings. As the conditioning set grows, CITs suffer from low statistical power, leading to frequent false negatives. In the context of structure learning, this causes error propagation that degrades the accuracy of the estimated graph. We propose DF-{PC} (Deduce-First {PC}), a theoretically sound framework that integrates graphoid-based reasoning into the {PC} algorithm. Unlike prior approaches that primarily utilize deduction for conflict resolution or additive checks, DF-{PC} adopts a proactive “Deduce-First” strategy: it prioritizes logical deduction from strictly lower-order tests to preemptively replace high-order CITs. This "Deduce-First" strategy enables structure learning with potentially fewer CITs while improving performance. Empirical evaluations across various settings demonstrate that DF-{PC} achieves competitive learning performance and computational efficiency.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26a/kim26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jonghwan family: Kim - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2958-2993 id: kim26a issued: date-parts: - 2026 - 8 - 6 firstpage: 2958 lastpage: 2993 published: 2026-08-06 00:00:00 +0000 - title: 'Beyond Bounds: Quantifying the Probability of Counterfactual Fairness' abstract: 'Counterfactual fairness is a rigorous criterion for algorithmic decision-making but remains fundamentally unidentifiable from observational data alone. Existing partial identification methods address this by deriving bounds for fairness measures; however, these intervals are often wide, limiting their practical utility. To address this limitation, we propose a framework that quantifies the probability that a black-box model satisfies counterfactual fairness, under a stated prior over the structural causal models compatible with the observed data. By exploiting conditional independencies to reduce the parameter space, we demonstrate that the set of causal parameters compatible with the observed data forms a convex polytope. We further show that, given domain-specific priors on exogenous distributions, this prior-dependent probability can be estimated via Hit-and-Run Monte Carlo integration. Our approach provides a practical tool that complements worst-case bounds, offering a prior-dependent probabilistic summary for auditing model fairness.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26b/kim26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Taehan family: Kim - given: Minyoung family: Cho - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 2994-3011 id: kim26b issued: date-parts: - 2026 - 8 - 6 firstpage: 2994 lastpage: 3011 published: 2026-08-06 00:00:00 +0000 - title: 'A Model-Free Universal AI' abstract: 'In general reinforcement learning, all established optimal agents, including {AIXI}, are model-based, explicitly maintaining and using environment models. This paper introduces Universal {AI} with {Q-Induction} ({AIQI}), the first model-free agent proven to be asymptotically $\varepsilon$-optimal in general {RL}. {AIQI} performs universal induction over distributional action-value functions, instead of policies or environments like previous works. Under a grain of truth condition, we prove that {AIQI} is strong asymptotically $\varepsilon$-optimal and asymptotically $\varepsilon$-{Bayes}-optimal. We also apply our novel proof techniques to show asymptotic $\varepsilon$-optimality of Self-{AIXI} without any ad-hoc assumptions. Our results significantly expand the diversity of known universal agents.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26c/kim26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yegon family: Kim - given: Juho family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3012-3035 id: kim26c issued: date-parts: - 2026 - 8 - 6 firstpage: 3012 lastpage: 3035 published: 2026-08-06 00:00:00 +0000 - title: 'Residual Koopman Spectral Profiling for Predicting and Preventing Transformer Training Instability' abstract: 'Training divergence in transformers wastes compute, yet practitioners discover instability only after expensive runs begin. They therefore need an initialization-time signal for identifying risky training configurations. We study Residual {Koopman} Spectral Profiling ({RKSP}), a fixed, single-forward-pass spectral risk score. {RKSP} extracts {Koopman} spectral features by applying whitened dynamic mode decomposition to layer-wise residual snapshots. Our central diagnostic, the near-unit spectral mass, quantifies the fraction of modes concentrated near the unit circle, which captures instability risk. For predicting divergence across extensive configurations, this score achieves an AUROC of 0.995, outperforming the best gradient baseline. When calibrated probabilities are required for a target configuration distribution, a held-out one-dimensional calibrator maps the same scalar score to probabilities. We further make the diagnostic actionable through {Koopman} Spectral Shaping ({KSS}), which reshapes spectra during training. In the challenging high learning rate regime without normalization layers, {KSS} reduces the divergence rate from 66.7% to 12.5% and enables learning rates that are 50% to 150% higher. Controlled experiments establish {RKSP} prediction and {KSS} intervention, real-data language modeling and vision experiments provide transfer evidence, and pretrained language-model profiling, including {GPT-2}, LLaMA-2, and {Qwen3}, demonstrates forward-only diagnostic scalability.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26d/kim26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bum Jun family: Kim - given: Shohei family: Taniguchi - given: Makoto family: Kawano - given: Yusuke family: Iwasawa - given: Yutaka family: Matsuo editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3036-3060 id: kim26d issued: date-parts: - 2026 - 8 - 6 firstpage: 3036 lastpage: 3060 published: 2026-08-06 00:00:00 +0000 - title: 'On Causal Representation Learning with Internal Auxiliaries' abstract: 'Causal representation learning typically achieves identifiability using auxiliary variables external to the mixing process. This fails when observable sources act as internal mixing inputs whose entanglement invalidates standard volume-change proofs. We introduce a framework that treats observable sources as internal auxiliaries. We establish identifiability when all observed internal sources are used as conditioning variables. Under a volume-preserving mixing assumption, suitable variability conditions, and additional alignment conditions on the learned model, the unobserved source subspaces are identifiable up to an Independent Subspace Analysis ({ISA})-style equivalence class—a permutation of conditionally independent subspaces with within-subspace invertible transformations. In practice, we approximate the volume-preserving restriction with encoders that stabilize the induced distortion. Leveraging the known causal graph, we further propose a scheme that selects conditioning sources so as to preserve fine-grained factorizations of the unobserved sources. Experiments show improved recovery over representative auxiliary-based baselines in settings where treating internal sources as external conditioners can induce cross-factor leakage.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26e/kim26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kwonho family: Kim - given: Heejeong family: Nam - given: Inwoo family: Hwang - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3061-3082 id: kim26e issued: date-parts: - 2026 - 8 - 6 firstpage: 3061 lastpage: 3082 published: 2026-08-06 00:00:00 +0000 - title: 'Model Merging is Secretly Certifiable: Non-Vacuous Generalisation Bounds for Low-Shot Learning' abstract: 'Certifying the IID generalisation ability of deep networks is the first of many requirements for trusting {AI} in high-stakes applications from medicine to security. However, when instantiating generalisation bounds for deep networks it remains challenging to obtain non-vacuous guarantees, especially when applying contemporary large models on the small scale data prevalent in such high-stakes fields. In this paper, we draw a novel connection between a family of learning methods based on model fusion and generalisation certificates, and surprisingly show that with minor adjustment several existing learning strategies already provide non-trivial generalisation guarantees. Essentially, by focusing on data-driven learning of downstream tasks by fusion rather than fine-tuning, the certified generalisation gap becomes tiny and independent of the base network size, facilitating its certification. Our results show for the first time non-trivial generalisation guarantees for learning with as low as 100 examples, while using vision models such as VIT-B and language models such as mistral-7B. This observation is significant as it has immediate implications for facilitating the certification of existing systems as trustworthy, and opens up new directions for research at the intersection of practice and theory.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26f/kim26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Taehoon family: Kim - given: Henry family: Gouk - given: Minyoung family: Kim - given: Timothy family: Hospedales editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3083-3100 id: kim26f issued: date-parts: - 2026 - 8 - 6 firstpage: 3083 lastpage: 3100 published: 2026-08-06 00:00:00 +0000 - title: 'Same Benchmark, Same Subspace: Task-Selective Convergence in LLM Representations' abstract: 'Benchmark scores are the dominant lens through which progress in large language models is assessed, yet the implicit assumption that different benchmarks read out a shared internal structure has never been verified at the representation level. We introduce readout subspace analysis, a framework that extracts the low-dimensional subspace a benchmark uses to linearly discriminate correct answers from a model’s frozen hidden representations, and compares these subspaces across models and tasks via a coordinate-invariant Gram cosine metric. Analyzing 50 models spanning six architecture families and varied fine-tuning strategies (SFT, DPO, RLHF, model merging) on three benchmarks (MMLU, MedQA, AGIEval), we find that readout geometry is governed by the benchmark, not the model. Within the same benchmark, readout subspaces are strongly aligned even across architecturally unrelated models (Gram cosine up to 0.87 versus a random baseline of ${\sim}10^{-3}$), while subspaces across different benchmarks are nearly orthogonal. This convergence is graded: benchmarks sharing cognitive demands partially overlap in readout subspace, whereas those requiring qualitatively different reasoning occupy orthogonal regions. Furthermore, probe accuracy consistently meets or exceeds generation accuracy, indicating that benchmark scores reflect not only representational structure but also decoding efficiency. These findings recast benchmarks from passive measurement instruments to active structural constraints that selectively activate specific regions of representation space.' volume: 337 URL: https://proceedings.mlr.press/v337/kim26g.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kim26g/kim26g.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kim26g.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: JaeSeong family: Kim - given: Suan family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3101-3116 id: kim26g issued: date-parts: - 2026 - 8 - 6 firstpage: 3101 lastpage: 3116 published: 2026-08-06 00:00:00 +0000 - title: 'Maximally Robust Satisficing Bayesian Optimization' abstract: 'Many design tasks can be cast as black-box function optimization, enabling use of {Bayesian} optimization to find an ideal design with minimal number of trials. However, often we do not actually need the optimum but instead a sufficiently good solution is enough, for instance a material that is durable enough for its intended use.In most cases there are multiple satisfactory solutions, forming a superlevel set of the function, raising a key question of which one to prefer. We answer this by explaining why robustness to input perturbations that may occur when the solution is deployed is a good criterion and by introduce a {Bayesian} optimization method that efficiently finds satisficing solutions that are robust to maximally large perturbations. In contrast to previous works, we assume the inputs can be accurately controlled during optimization, but will be perturbed after the deployment.' volume: 337 URL: https://proceedings.mlr.press/v337/kinnunen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kinnunen26a/kinnunen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kinnunen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Samuli family: Kinnunen - given: Petrus family: Mikkola - given: Antti family: Niskanen - given: Arto family: Klami editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3117-3142 id: kinnunen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3117 lastpage: 3142 published: 2026-08-06 00:00:00 +0000 - title: 'Controlling Uncertainty and Hallucination Risk in Multi-Agent Fact Verification' abstract: 'Multi-agent language systems are increasingly relied upon for high-stakes decision support. Many systems use consensus among agents as a measure of confidence. However, such a model is prone to failure if aligned agents have the same biases and propagate the same error. Under sycophantic consensus, correlated errors resemble strong agreement, and hallucination manifests as a consequence of uncalibrated uncertainty. While current measures provide useful heuristics, they lack statistical safety bounds at deployment time. This work reinterprets hallucination control as an uncertainty quantification problem. We contribute a Score Deviation penalty that directly lowers confidence when the factual disagreement within the ensemble rises. A Learn-Then-Test calibration procedure converts these penalized scores into a certified decision threshold that provably bounds the expected False Discovery Rate. The results show that this deviation-penalized method reduces the conservatism of the calibration process, achieving 71.7% recall compared to 47.4% for naive baselines at a strict 2% risk budget.' volume: 337 URL: https://proceedings.mlr.press/v337/kostka26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kostka26a/kostka26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kostka26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Adam family: Kostka - given: Jaroslaw A. family: Chudziak editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3143-3161 id: kostka26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3143 lastpage: 3161 published: 2026-08-06 00:00:00 +0000 - title: 'Who to Trust? Aggregating Client Predictions in Federated Distillation.' abstract: 'Federated Distillation enables distributed learning for clients with heterogeneous model architectures. In this paradigm, the server and clients exchange predictions on a shared unlabeled public dataset, rather than model parameters or gradients. % However, under data heterogeneity (e.g., class mismatch), clients produce unreliable predictions for instances from unfamiliar classes. % An equally weighted combination of such predictions corrupts the teacher signal used for distillation. % In this paper, we theoretically analyze Federated Distillation and show that aggregating client predictions on a shared public dataset converges to a neighborhood of the optimum, with the neighborhood size controlled by the aggregation quality. % We propose two uncertainty-aware aggregation methods, $\textbf{UWA}$ and $\textbf{sUWA}$, that use density-based estimates to down-weight unreliable client predictions. % Experiments on image and text classification datasets confirm that our methods are most effective under high data heterogeneity, while matching standard averaging when heterogeneity is low.' volume: 337 URL: https://proceedings.mlr.press/v337/kovalchuk26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kovalchuk26a/kovalchuk26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kovalchuk26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Viktor family: Kovalchuk - given: Denis family: Son - given: Arman family: Bolatov - given: Mohsen family: Guizani - given: Samuel family: Horváth - given: Maxim family: Panov - given: Martin family: Takáč - given: Eduard family: Gorbunov - given: Nikita family: Kotelevskii editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3162-3181 id: kovalchuk26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3162 lastpage: 3181 published: 2026-08-06 00:00:00 +0000 - title: 'Decomposing Ensemble Spread in Lorenz ’96 with Learned Stochastic Parameterizations' abstract: 'Weather and climate forecasts are inherently uncertain due to chaotic dynamics, imperfect initial conditions, and incomplete representation of the underlying physical processes. Operational ensemble forecasts aim to represent these uncertainties through forecast spread, yet many approaches yield underdispersive estimates, with spread that grows too slowly relative to forecast error. Using the two-scale {Lorenz} ’96 system as a widely used, controlled testbed, we design a systematic approach to disentangle intrinsic variability, initial-condition perturbations, and stochastic model uncertainty. We compare multiple ensemble configurations and parameterization strategies, including existing deterministic and autoregressive as well as novel {Bayesian} and flow-based approaches. Our results show that ensemble perturbations do not increase the system’s long-term variance; rather, they regulate how rapidly trajectories decorrelate and explore the invariant measure. Stochastic parameterizations, particularly those with temporally persistent structure, enhance early spread growth and improve spread-error consistency. Overall, we bring clarity to how different sources of uncertainty interact in a chaotic system and provide guidance for the design and evaluation of stochastic parameterizations in weather and climate models.' volume: 337 URL: https://proceedings.mlr.press/v337/kuhbacher26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kuhbacher26a/kuhbacher26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kuhbacher26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Birgit family: Kühbacher - given: Daan family: Crommelin - given: Niki family: Kilbertus editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3182-3223 id: kuhbacher26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3182 lastpage: 3223 published: 2026-08-06 00:00:00 +0000 - title: 'Controlling Path Dependence in Gradient Ascent Unlearning through Forget-Set Ordering' abstract: 'Machine unlearning aims to selectively remove the influence of designated training data from a trained model. Gradient ascent-based unlearning methods are widely used in machine unlearning, but are often observed to exhibit instability and sensitivity to optimization hyperparameters. In this work, we show that the ordering of forget-set samples during ascent materially influences the resulting optimization trajectory, yielding markedly different forgetting–retention trade-offs under identical optimization budgets. We provide a local second-order analysis illustrating how non-commutativity of ascent updates induces path dependence, and we propose a simple ordering strategy that processes forget samples from low to high predictive uncertainty. By deferring high-uncertainty samples, this strategy attenuates early parameter drift and leads to more stable trajectories. Across image classification benchmarks with convolutional and vision transformer architectures, as well as text classification tasks, we observe that this ordering consistently achieves effective forgetting while better preserving retain-set utility compared to random ordering. In the retain-data-free regime, this trajectory-aware modification substantially strengthens vanilla gradient ascent, improving its position on the forgetting–retention Pareto frontier relative to naive ascent and several retain-data-free unlearning baselines. In general, our results identify sample ordering as a practically meaningful and previously under explored degree of freedom in machine unlearning, highlighting the importance of trajectory-aware design and evaluation.' volume: 337 URL: https://proceedings.mlr.press/v337/kumar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/kumar26a/kumar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-kumar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Varun Sampath family: Kumar - given: Esmaeil S. family: Nadimi - given: Vinay Chakravarthi family: Gogineni editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3224-3236 id: kumar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3224 lastpage: 3236 published: 2026-08-06 00:00:00 +0000 - title: 'KMM-CP: Practical Conformal Prediction under Covariate Shift via Selective Kernel Mean Matching' abstract: 'Uncertainty quantification is essential for deploying machine learning models in high-stakes domains such as scientific discovery and healthcare. Conformal Prediction ({CP}) provides finite-sample coverage guarantees under exchangeability, an assumption often violated in practice due to distribution shift. Under covariate shift, restoring validity requires importance weighting, yet accurate density-ratio estimation becomes unstable when training and test distributions exhibit limited support overlap. We propose KMM-{CP}, a conformal prediction framework based on Kernel Mean Matching (KMM) for covariate-shift correction. We show that KMM directly controls the bias–variance components governing conformal coverage error by minimizing RKHS moment discrepancy under explicit weight constraints, and establish asymptotic coverage guarantees under mild conditions. We then introduce a selective extension that identifies regions of reliable support overlap and restricts conformal correction to this subset, further improving stability in low-overlap regimes. Experiments on molecular property prediction benchmarks with realistic distribution shifts show that KMM-{CP} reduces coverage gap by over 50% compared to existing approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/laghuvarapu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/laghuvarapu26a/laghuvarapu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-laghuvarapu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Siddhartha family: Laghuvarapu - given: Rohan family: Deb - given: Jimeng family: Sun editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3237-3261 id: laghuvarapu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3237 lastpage: 3261 published: 2026-08-06 00:00:00 +0000 - title: 'Robustness Quantification for Discriminative Models: a New Robustness Metric and its Application to Dynamic Classifier Selection' abstract: 'Among the different possible strategies for evaluating the reliability of individual predictions of classifiers, robustness quantification stands out as a method that evaluates how much uncertainty a classifier could cope with before changing its prediction. However, its applicability is more limited than some of its alternatives, since it requires the use of generative models and restricts the analyses either to specific model architectures or discrete features. In this work, we propose a new robustness metric applicable to any probabilistic discriminative classifier and any type of features. We demonstrate that this new metric is capable of distinguishing between reliable and unreliable predictions, and use this observation to develop new strategies for dynamic classifier selection.' volume: 337 URL: https://proceedings.mlr.press/v337/lassance26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lassance26a/lassance26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lassance26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Rodrigo F L family: Lassance - given: Jasper family: De Bock editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3262-3273 id: lassance26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3262 lastpage: 3273 published: 2026-08-06 00:00:00 +0000 - title: 'Task-Free Continual Learning via Order-Invariant Linearized Adaptation and Density-Guided Adapter Routing' abstract: 'Task-free continual learning (TFCL) aims to adapt models to non-stationary data streams without knowing task boundaries. In TFCL, catastrophic forgetting arises from both the evolving data distributions and the order-sensitive nature of batch-streaming optimization. To address these challenges, we propose a new TFCL framework that mitigates optimization-induced forgetting via order-invariant linearized adaptation during learning and accommodates evolving data distributions via density-guided adapter routing for more accurate and effective adapter retrieval during inference. We also provide a theoretical characterization of retrieval error in terms of density estimation quality and cross-adapter embedding separability. Experiments across multiple benchmarks demonstrate that our proposed method consistently achieves higher accuracy and lower forgetting than strong TFCL baselines under both standard and realistic streaming settings. For reproducibility, our experimental code is available at: https://github.com/Alisia0303/HESTIA.git .' volume: 337 URL: https://proceedings.mlr.press/v337/le26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/le26a/le26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-le26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hang Thi-Thuy family: Le - given: Nam-Quan family: Nguyen - given: Lam-Huy family: Nguyen - given: Dien family: Dinh - given: Minh family: Hoang - given: Trong Nghia family: Hoang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3274-3297 id: le26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3274 lastpage: 3297 published: 2026-08-06 00:00:00 +0000 - title: 'Efficient Confidence Set Enumeration for Multi-label Conformal Classification' abstract: 'Conformal prediction is a distribution-free and model agnostic framework that can provide statistical guarantees to machine learning algorithms: a point-wise predictor is transformed into a conformal predictor that outputs sets of predictions which include the ground truth with a user defined confidence rate. In multi-label conformal classification however, the exponential growth of the output space makes confidence sets prohibitively complex to compute in the general case. In this paper, we analyze this challenge under the prism of enumeration complexity. We detail a general approach for confidence set enumeration based on the flashlight method, prove a sufficient condition for efficient enumeration and apply this method on three types of problems. First, we give an enumeration algorithm with linear delay for modular non-conformity losses. Then, we discuss informed conformal classification where a boolean circuit specifies a set of valid label combinations and prove a sufficient condition for efficient enumeration based on standard properties of the circuit. Moreover, we leverage our results on informed conformal classification to tackle label interactions in the loss. Finally, we illustrate the benefits of our approach with a few experiments.' volume: 337 URL: https://proceedings.mlr.press/v337/ledaguenel26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ledaguenel26a/ledaguenel26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ledaguenel26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Arthur family: Ledaguenel - given: Florent family: Capelli - given: Jean-Marie family: Lagniez editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3298-3322 id: ledaguenel26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3298 lastpage: 3322 published: 2026-08-06 00:00:00 +0000 - title: 'Provably Correct $k$-Means Clustering of Persistence Diagrams' abstract: 'We study $k$-means clustering of persistence diagrams through their {Hilbert}-space embeddings, focusing primarily on persistence landscapes. Although persistence landscapes are widely used in practice, it remains unclear when clustering them faithfully reflects clustering in the diagram space. We give simple, verifiable geometric conditions under which (i) nearest-center labels in the landscape space exactly agree with those in the diagram space, and (ii) the landscape $k$-means objective provably calibrates the diagram-space objective, leveraging tools from modern statistical learning theory. Combined with known fast rates for $k$-means in {Hilbert} spaces, our results show that landscape-based $k$-means provides a statistically and computationally efficient surrogate for diagram-space $k$-means with explicit performance guarantees and a controllable geometric distortion.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26a/lee26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hajin family: Lee - given: Kwangho family: Kim editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3323-3337 id: lee26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3323 lastpage: 3337 published: 2026-08-06 00:00:00 +0000 - title: 'High-Order Markov Blanket Discovery via a k-Order Relaxation of the Faithfulness Assumption' abstract: 'The problem of learning the graphical {Markov} blanket (MB) of a variable from data has applications in many areas such as structure learning for {Bayesian} networks and {Markov} random fields, causal discovery, and feature selection. However, a common assumption most methods make is that the conditional independencies in the distribution imply the same separation in the graphical structure—also known as the faithfulness assumption. Unfortunately, this assumption can be violated by higher-order dependencies such as {XOR} and parity-type relations, and—on finite samples—by empirical violations that, in extreme cases, even induce spurious dependencies absent from the true distribution. Therefore, in this paper we propose a “k-order” relaxation of the faithfulness assumption that captures parity type relationships between k+2 variables. We then propose a proof of concept algorithm called k-order {Markov} blanket (kOMB) that uses this relaxation for MB discovery. Finally, we empirically show how kOMB can recover the MB of a variable under both true and empirical violations of faithfulness. Code available at: https://github.com/lklee9/k-order-{Markov}-blanket.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26b/lee26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Loong Kuan family: Lee - given: Ragavi family: Krishnamoorthy - given: Nico family: Piatkowski editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3338-3354 id: lee26b issued: date-parts: - 2026 - 8 - 6 firstpage: 3338 lastpage: 3354 published: 2026-08-06 00:00:00 +0000 - title: 'Nonlocal Bayesian Modeling of Continuous Spatio-Temporal Dynamics' abstract: 'Real-world spatio-temporal forecasting must handle irregular time points, spatially sparse observations, and the need for uncertainty quantification. This setting is often further compounded by nonlocal interactions (long-range spatial coupling). Modeling continuous-space, continuous-time nonlocal dynamics naturally leads to infinite-dimensional integro-differential equations (IDEs), making principled {Bayesian} inference intractable. We propose the NonLocal {Bayesian} Spatio-Temporal model (NLBST), a hierarchical {Bayesian} framework for continuous spatio-temporal fields that learns explicit nonlocal coupling while retaining tractable inference. NLBST represents the latent field via a coordinate-based spatial basis expansion and models the coefficient process with a continuous-time {ODE} whose learnable linear operator corresponds to a Galerkin reduction of a nonlocal IDE; a Neural {ODE} residual captures additional nonlinear dynamics. A linear-{Gaussian} observation model enables {Kalman}-style sequential updates under missing and irregular observations, while the spatial basis representation enables inductive prediction at unmeasured locations without retraining. Global parameters are learned via variational inference, and uncertainty is handled through a {Bayesian} hierarchy. Experiments on synthetic and real-world datasets demonstrate strong forecasting and spatial generalization with well-calibrated uncertainty, yielding substantial gains over baselines in strongly nonlocal and partially observed regimes.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26c/lee26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jaeyeong family: Lee - given: Heeyoung family: Kim editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3355-3375 id: lee26c issued: date-parts: - 2026 - 8 - 6 firstpage: 3355 lastpage: 3375 published: 2026-08-06 00:00:00 +0000 - title: 'Interpretable Spatial-Temporal Forecasting via Additive Neural Decomposition and Knowledge Distillation' abstract: 'We challenge the prevailing assumption that interpretability requires sacrificing accuracy in spatial-temporal forecasting. We propose STGNAM (Spatial-Temporal Graph Neural Additive Model), which enforces a strict additive decomposition: $\hat{\mathbf{y}} = f_{\text{node}} + f_{\text{temporal}} + f_{\text{spatial}} + f_{\text{interact}} + \text{bias}$, where each component is independently evaluable and visualizable. Our central finding is that the additive inductive bias acts as an implicit regularizer: on PEMS-BAY, STGNAM *sets a new state of the art* (MAE $1.62$), surpassing all black-box models including TITAN ($1.69$) and its own D2STGNN teacher ($1.87$)—even without knowledge distillation (KD). When combined with KD from a black-box teacher, STGNAM achieves $91$–$104%$ of SOTA across five benchmarks while providing full additive interpretability. KD also produces a secondary benefit: component-level faithfulness increases from $0.53$ to $0.92$ on METR-LA, and skip connection dominance drops from $65%$ to $43%$, indicating that soft-target supervision forces additive components to learn structured, specialized representations. We validate this through direct comparison with post-hoc attribution methods (gradient saliency, SmoothGrad), showing that inherent additive explanations are more faithful and stable than post-hoc alternatives applied to black-box models.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26d/lee26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Suan family: Lee - given: Jinho family: Kim editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3376-3397 id: lee26d issued: date-parts: - 2026 - 8 - 6 firstpage: 3376 lastpage: 3397 published: 2026-08-06 00:00:00 +0000 - title: 'FraudGNAM: Inherently Interpretable Spectral GNN for Graph Fraud Detection' abstract: 'Graph neural networks for fraud detection face a fundamental tension: spectral methods that capture heterophilic patterns sacrifice interpretability, while interpretable models lack the spectral capacity to detect sophisticated fraud. We introduce {FraudGNAM} (Fraud Graph Neural Additive Model), the first inherently interpretable spectral GNN with learnable multi-scale filters that resolves this tension. {FraudGNAM} decomposes the fraud score into individually auditable components—per-feature contributions via neural additive models, pairwise feature interactions, multi-scale spectral band responses via learnable polynomial filters, and explicit feature-spectrum interactions—all combined through a transparent scalar-sum architecture. Each component’s contribution to the final prediction is independently quantifiable, unlike post-hoc explanation methods that approximate black-box decisions. On seven GADBench datasets spanning homophily ratios from 0.60 to 0.98, {FraudGNAM} achieves state-of-the-art AUROC on five of seven datasets against SEC-GFD, the strongest black-box baseline, while winning 14 of 21 metric-dataset comparisons overall. An adaptive configuration mechanism selects spectral order, high-pass filter count, and contrastive regularization based on measurable graph properties, eliminating per-dataset hyperparameter search.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26e/lee26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Suan family: Lee - given: Jinho family: Kim editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3398-3428 id: lee26e issued: date-parts: - 2026 - 8 - 6 firstpage: 3398 lastpage: 3428 published: 2026-08-06 00:00:00 +0000 - title: 'Preserving Compositionality for Robust Multi-Subject Personalization in Text-to-Image Generation' abstract: 'Personalized text-to-image generation faces a fundamental trade-off between learning new concepts and preserving existing knowledge, and balancing these two goals gets particularly more challenging with multiple subjects to be personalized. Existing methods have relieved this by providing additional layout constraints, but it substantially undermines flexibility of the generation process. To address this issue, we propose a teacher–student architecture equipped with explicit regularizers to mitigate this trade-off. Specifically, we regulate the internal representations and cross-attention maps not to significantly deviate from the original foundation model, balanced with the reconstruction objective to internalize new concepts. Through extensive experiments, we demonstrate that our method enables reliable layout-free multi-subject generation, achieving the state-of-the-art performance on both single- and multi-concept personalization.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26f/lee26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sangho family: Lee - given: Eugene family: Baek - given: Suho family: Ryu - given: Dongsoo family: Shin - given: Joonseok family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3429-3452 id: lee26f issued: date-parts: - 2026 - 8 - 6 firstpage: 3429 lastpage: 3452 published: 2026-08-06 00:00:00 +0000 - title: 'Diagnosing Conformal Prediction Failures Under Distribution Shift: A COVID-19 Case Study' abstract: 'Conformal prediction provides distribution-free coverage guarantees, but these degrade under distribution shift—and practitioners lack tools to anticipate which deployed models will fail before observing test data. We propose SHapley Additive exPlanations (SHAP) concentration—the fraction of feature importance concentrated in the top feature—as a pre-deployment diagnostic for conformal prediction vulnerability in gradient-boosted classifiers. Using COVID-19 as a naturalistic case study, eight supply chain tasks experience identical temporal shift yet coverage drops ranging from negligible to catastrophic. Feature-importance concentration is strongly associated with failure severity across 16 multiclass tasks in 9 domains, while standard distributional shift detectors detect shift uniformly across tasks but cannot distinguish catastrophic from robust outcomes. External validation across 9 non-supply-chain datasets shows partial transfer. We prove a formal theorem showing that Adaptive Prediction Sets conformity-score bounds worsen monotonically with concentration under explicit assumptions, verified empirically. The diagnostic identifies concentrated-dependence failures characteristic of gradient-boosted models but does not detect global-sensitivity failures observed in neural networks. A decision framework operationalizes the diagnostic as an exploratory pre-deployment rule with an uncertainty band around a concentration threshold.' volume: 337 URL: https://proceedings.mlr.press/v337/lee26g.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lee26g/lee26g.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lee26g.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Chorok family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3453-3476 id: lee26g issued: date-parts: - 2026 - 8 - 6 firstpage: 3453 lastpage: 3476 published: 2026-08-06 00:00:00 +0000 - title: 'Counting and Sampling Subsets Using Block Covers' abstract: 'We present a new data structure, *block cover*, for approximate weighted counting and sampling of subsets of a given query set. Such queries are the main computational bottleneck, e.g., in advanced {Markov} chain Monte Carlo algorithms for {Bayesian} learning of {Bayesian} networks. Given a collection of weighted subsets of a ground set $N$, our key idea is to select a few moderate-size subsets $B$ of $N$, called blocks, so as to cover all or most of the input collection by the power sets $2^B$. An approximate sum over the subsets of a query set $Q$ is obtained by adding up the contributions within each block, which contibutions we precompute. We also give a similar, efficient algorithm for generating a subset of $Q$ with probability proportional to its weight. Our empirical results suggest that block covers are superior to previous approaches, which consider the subsets of interest one by one.' volume: 337 URL: https://proceedings.mlr.press/v337/lehtinen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lehtinen26a/lehtinen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lehtinen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Elias family: Lehtinen - given: Mikko family: Koivisto editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3477-3486 id: lehtinen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3477 lastpage: 3486 published: 2026-08-06 00:00:00 +0000 - title: 'Gaussian Approximation and Multiplier Bootstrap for Federated Linear Stochastic Approximation' abstract: 'In this paper, we establish Berry-Esseen-type bounds for federated linear stochastic approximation (LSA). Our results provide the first federated {Gaussian} approximations for LSA that explicitly capture communication-computation trade-offs and heterogeneity-aware error terms, quantifying the effects of local step size, number of local updates, and heterogeneity on convergence rates. We present results for both (i) constant step size regime and (ii) decreasing step size with an increasing number of local iterations, recovering the recent rates of Bonnerjee et al. [2026] as a special case. As a primary application of our results, we develop an online multiplier bootstrap procedure for inference on the last iterate, which avoids explicit estimation of the asymptotic covariance matrix, and obtain non-asymptotic validity guarantees for this procedure.' volume: 337 URL: https://proceedings.mlr.press/v337/levin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/levin26a/levin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-levin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ilya family: Levin - given: Maksim family: Shuklin - given: Eric family: Moulines - given: Paul family: Mangold - given: Sergey family: Samsonov editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3487-3545 id: levin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3487 lastpage: 3545 published: 2026-08-06 00:00:00 +0000 - title: 'Computational Complexity of Repair Problems on Simple Temporal Networks with Uncertainty' abstract: 'Simple Temporal Networks with Uncertainty (STNUs) are a well-established formalism for reasoning about temporal plans involving uncontrollable durations, known as contingent links. This model enables checking the controllability of plans under different assumptions about when uncertainties are revealed (Weak, Dynamic, and Strong Controllability). Recent work has also introduced methods to repair uncontrollable STNUs by adjusting contingent bounds, which is relevant e.g., in multi-agent systems, or resource-aware settings where some external flexibility can be negotiated. Nevertheless, there remains a lack of formal understanding regarding the computational complexity of such repair problems. This paper fills that gap by formally defining the problems and assessing the complexity of a number of them. In particular, we show that for a number of settings, repair is no harder than controllability.' volume: 337 URL: https://proceedings.mlr.press/v337/li26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26a/li26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Junkang family: Li - given: Frédéric family: Maris - given: Ajdin family: Sumic - given: Thierry family: Vidal - given: Bruno family: Zanuttini editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3546-3555 id: li26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3546 lastpage: 3555 published: 2026-08-06 00:00:00 +0000 - title: 'Differentially Private Approval-Based Committee Voting' abstract: 'In this paper, we investigate tradeoffs among differential privacy ({DP}) and several representative axioms for approval-based committee voting, including justified representation, proportional justified representation, extended justified representation, Pareto efficiency, and Condorcet criterion. Without surprise, we demonstrate that all of these axioms are incompatible with {DP}, and thus establish both upper and lower bounds for their two-way tradeoffs with {DP}. Furthermore, we provide upper and lower bounds for three-way tradeoffs among {DP} and every pairwise combination of such axioms, revealing that although these axioms are compatible without {DP}, their optimal levels under {DP} cannot be simultaneously achieved. Our results quantify the effect of {DP} on the satisfaction and compatibility of the axioms in approval-based committee voting, which can provide insights for designing voting rules that possess both privacy and axiomatic properties.' volume: 337 URL: https://proceedings.mlr.press/v337/li26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26b/li26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhechen family: Li - given: Zimai family: Guo - given: Lirong family: Xia - given: Yongzhi family: Cao - given: Hanpin family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3556-3580 id: li26b issued: date-parts: - 2026 - 8 - 6 firstpage: 3556 lastpage: 3580 published: 2026-08-06 00:00:00 +0000 - title: 'Nonlinear Axiomatic Attribution for Cooperative Games' abstract: 'The {Shapley} value is a widely used concept in attribution problems, as it uniquely satisfies the axioms of linearity, consistency, equal treatment, and efficiency. Often, the inclusion AUC metric is used to evaluate the quality of player rankings, in order to identify positively participating players. However, it can be established that the {Shapley} value is not always reliable for this purpose. The core issue lies in its linearity: the {Shapley} value acts as a linear operator with an excessively large null space, which is likely to contain non-negligible perturbations that remain indistinguishable to the operator. To address this limitation, we explore the design of nonlinear axiomatic attribution methods. Inspired by the least core, which is a popular nonlinear substitute for the {Shapley} value, we introduce a class of nonlinear attribution methods that retain the remaining necessary axioms. Each method yields a contribution vector that is the unique optimal solution to a minimization problem, which aims to approximate utility functions as faithfully as possible. In terms of the inclusion AUC metric, our experiments demonstrate the potential effectiveness of these methods compared to {Shapley} value variants that relax only the efficiency axiom.' volume: 337 URL: https://proceedings.mlr.press/v337/li26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26c/li26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Weida family: Li - given: Zhuanghua family: Liu - given: Yaoliang family: Yu - given: Bryan Kian Hsiang family: Low editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3581-3603 id: li26c issued: date-parts: - 2026 - 8 - 6 firstpage: 3581 lastpage: 3603 published: 2026-08-06 00:00:00 +0000 - title: 'Matched-Pair Experimental Design with Active Learning' abstract: 'Matched-pair experimental designs aim to detect treatment effects by pairing participants and comparing within-pair outcome differences. In many situations, the overall effect size across the entire population is small. Then, the focus naturally shifts to identifying and targeting high treatment-effect regions where the intervention is most effective. This paper proposes a matched-pair experimental design that sequentially and actively enrolls patients in high treatment-effect regions. Importantly, we frame the identification of the target region as a classification problem and propose an active learning framework tailored to matched-pair designs. Our design not only reduces the experimental cost of detecting treatment efficacy, but also ensures that the identified regions enclose the entire high-treatment-effect regions. Our theoretical analysis of the framework’s label complexity and experiments in practical scenarios demonstrate the efficiency and advantages of the approach.' volume: 337 URL: https://proceedings.mlr.press/v337/li26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26d/li26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Weizhi family: Li - given: Gautam family: Dasarathy - given: Visar family: Berisha editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3604-3630 id: li26d issued: date-parts: - 2026 - 8 - 6 firstpage: 3604 lastpage: 3630 published: 2026-08-06 00:00:00 +0000 - title: 'Leveraging Large Language Models for Causal Discovery: a Constraint-based, Argumentation-driven Approach' abstract: 'Causal discovery seeks to uncover causal relations from data, typically represented as causal graphs, and is essential for predicting the effects of interventions. While expert knowledge is required to construct principled causal graphs, many statistical methods have been proposed to leverage observational data with varying formal guarantees. Causal Assumption-based Argumentation (ABA) is a framework that uses symbolic reasoning to ensure correspondence between input constraints and output graphs, while offering a principled way to combine data and expertise. We explore the use of large language models ({LLMs}) as imperfect experts, eliciting semantic structural constraints from variable names and descriptions and integrating them with statistical evidence through Causal ABA. We propose ABAPC-{LLM} as a principled and conservative approach to hybrid data- and {LLM}-driven causal discovery. Additionally, we introduce an evaluation protocol to mitigate memorisation bias when assessing {LLMs} for causal discovery and show competitive performance on novel semantically grounded random benchmarks, as well as on standard small- and medium-sized benchmarks.' volume: 337 URL: https://proceedings.mlr.press/v337/li26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26e/li26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zihao family: Li - given: Fabrizio family: Russo editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3631-3667 id: li26e issued: date-parts: - 2026 - 8 - 6 firstpage: 3631 lastpage: 3667 published: 2026-08-06 00:00:00 +0000 - title: 'Online Fair Allocation with Demand-Side Time-Dependent Weight' abstract: 'We study the problem of allocating indivisible items to a group of agents as these items arrive over time. Our focus is on scenarios where the utility of the items is weighted based on the waiting time since the last item was received, which is a demand-side time-dependent utility model. To ensure fairness, we concentrate on two criteria: temporal envy-freeness (TEF) and temporal proportionality (TProp). These criteria require that the allocation remains fair after each item is allocated. When there are two agents, we demonstrate the sufficient and necessary conditions of the weight function that ensure the existence of a TEF1 or TProp1 allocation. Additionally, we provide two polynomial-time algorithms that output a TEF2 or TProp2 allocation, with some restrictions on the weight function. When there are more than two agents, we show the hardness of determining the existence of TEF1 allocations. We also provide polynomial algorithms returning TEF1/TProp1 allocations with some specific valuation profiles. When there are multiple items per round, we also provide a polynomial algorithm returning TEF1/TProp1 allocations.' volume: 337 URL: https://proceedings.mlr.press/v337/li26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26f/li26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Minming family: Li - given: Youzhi family: Zhang - given: Shangkun family: Zheng editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3668-3684 id: li26f issued: date-parts: - 2026 - 8 - 6 firstpage: 3668 lastpage: 3684 published: 2026-08-06 00:00:00 +0000 - title: 'A Sequence-Graph Fusion Framework via BiMamba and Fourier-KAN for Interpretable Drug-Target Affinity Prediction' abstract: 'Accurate prediction of drug-target affinity (DTA) is crucial for accelerating drug discovery. Existing methods struggle to model global long-range dependencies of sequences at linear complexity, and multi-layer perceptrons relying on fixed activation functions in graph neural networks face limitations in fitting complex non-linear topologies. We propose SGFF-DTA, a sequence-graph fusion framework based on bidirectional Mamba ({BiMamba}) and {Fourier}-{Kolmogorov}-Arnold Networks ({Fourier-KAN}). The framework employs {BiMamba} to capture global contextual semantics of sequences at linear complexity through bidirectional selective state space scanning. It integrates {Fourier-KAN} into graph neural networks to model high-order topological interactions using learnable non-linear transformations in the spectral space. To achieve cross-modal semantic alignment, we introduce pre-trained feature transfer and a cross-gated fusion module. On three benchmark datasets, SGFF-DTA significantly outperforms state-of-the-art methods in terms of mean squared error, demonstrating robust generalization capabilities under cold-start settings. Visual analysis further confirms model interpretability in accurately locating key binding sites and pharmacophores.' volume: 337 URL: https://proceedings.mlr.press/v337/li26g.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26g/li26g.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26g.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xibo family: Li - given: Lian family: Chen - given: Dingyuan family: Chen - given: Yichuan family: Zhao - given: Li family: Zhou - given: Dongxi family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3685-3704 id: li26g issued: date-parts: - 2026 - 8 - 6 firstpage: 3685 lastpage: 3704 published: 2026-08-06 00:00:00 +0000 - title: 'CAIC: Congestion-Aware Intent Communication for Multi-Agent Reinforcement Learning' abstract: 'In multi-agent reinforcement learning, communication is essential for effective cooperation. Most existing methods assume instantaneous message delivery, and the few delay-aware studies consider only external fixed or stochastic delays, neglecting queueing delays caused by competition for a shared channel. We formulate the shared channel as a queueing system with state-dependent service rates, and propose Congestion-Aware Intent Communication ({CAIC}). To ensure message validity under delay, {CAIC} employs a temporal masked autoencoder to predict each agent’s future trajectory and encode it into a delay-robust intent message, with attention-based fusion integrating asynchronous messages at the receiver. To maintain timeliness, {CAIC} dynamically adjusts communication frequency based on intent message changes and delay estimates, proactively mitigating congestion. Experiments on Hallway, MPE, and SMAC demonstrate that {CAIC} outperforms existing baselines on most evaluated scenarios in both no-delay and queueing-delay settings, and ablation studies reveal that stale messages under delay can be even more harmful than no communication.' volume: 337 URL: https://proceedings.mlr.press/v337/li26h.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26h/li26h.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26h.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Pei family: Li - given: Yongkang family: Zhang - given: Zhonglin family: Lv - given: Jinmin family: Zhu - given: Jiangjin family: Yin editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3705-3718 id: li26h issued: date-parts: - 2026 - 8 - 6 firstpage: 3705 lastpage: 3718 published: 2026-08-06 00:00:00 +0000 - title: 'Label-Wise uncertainty decomposition for Multi-label Classification by Maximizing Type II Likelihood' abstract: 'Currently, the way deep learning models recognize uncertainty remains inconsistent with human perception. In multi-label classification, quantifying uncertainty at the label level presents challenges, as each label may exhibit distinct model confidence levels. Understanding and decomposing label-specific uncertainty is essential for interpreting model behavior and ensuring reliable predictions. We build a hierarchical {Bayesian} methodology for multi-label classification that leverages a Type {II} likelihood and Empirical {Bayes}. Then we estimate and decompose label-wise uncertainties by the bias-variance decomposition. Our approaches offer four main contributions: (1) Type {II} likelihood maximization is data likelihood centric; (2) it can decompose label-wise uncertainty into the model variance, the model bias and data noise; (3) our uncertainty represented by model bias is intuitively interpretable when combined with observational data; and (4) when applied to out-of-distribution ({OOD}) detection task, it achieves a 6.88% lower FPR95 score on NUS-WIDE.' volume: 337 URL: https://proceedings.mlr.press/v337/li26i.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26i/li26i.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26i.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Minghao family: Li - given: Junjie family: Qiu - given: Weishi family: Shi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3719-3737 id: li26i issued: date-parts: - 2026 - 8 - 6 firstpage: 3719 lastpage: 3737 published: 2026-08-06 00:00:00 +0000 - title: 'Remedying Coarsening-Based GNN Training under Heterophily via Adaptive Complementary Enhancement' abstract: 'Coarsening-based training for graph neural networks (GNNs), i.e. training on coarsened graphs rather than the original large ones, has become a promising direction for scaling GNNs to massive graphs. However, prior work has been evaluated almost exclusively on *homophilic* graphs, leaving the more challenging *heterophilic* settings underexplored. We show, both empirically and theoretically, that existing coarsening-based training methods suffer significant performance degradation on heterophilic graphs due to inevitable loss of graph information during coarsening. To address this, we propose **A**daptive **C**omplementary **E**nhancement, a plug-and-play, model-agnostic strategy that reintegrates the information discarded in coarsening: ACE learns a projector for re-constructing original node features and applies *anisotropic structural regularization* to embed local heterophily. We further adopt *homoscedastic uncertainty weighting* to adaptively balance the combined training objective of primary coarsened-graph training loss and full-graph auxiliary loss with augmented node features re-constructed by the heterophily-aware projector. Extensive experiments show that ACE drives consistent gains on heterophilic benchmarks while preserving competitive results on homophilic graphs with minimal computational overhead. Code is available at the {GitHub} repository: \url{ https://github.com/vasile-paskardlgm/ACE }.' volume: 337 URL: https://proceedings.mlr.press/v337/li26j.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26j/li26j.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26j.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Guoming family: Li - given: Jian family: Yang - given: Xukun family: Wang - given: Zixiao family: Wang - given: Shangsong family: Liang - given: Yifan family: Chen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3738-3761 id: li26j issued: date-parts: - 2026 - 8 - 6 firstpage: 3738 lastpage: 3761 published: 2026-08-06 00:00:00 +0000 - title: 'Exploiting Concavity Information in Contextual Bandit Optimization' abstract: 'The contextual bandit models sequential decision-making problems in which rewards depend on both the chosen action and observed context. In many domains such as medicine, business, and engineering, prior knowledge provides structural information about the reward function that can be exploited to improve optimization efficiency. This paper studies settings where, for each observable context, the conditional mean reward is known to be concave with respect to the action variable. To leverage this structure, we develop a contextual bandit algorithm that conditions a {Bayesian} {Gaussian} Process posterior on concavity constraints. We propose a novel reward model that combines a concavity-preserving regression spline basis with a constrained GP posterior, yielding a tractable shape-constrained estimator. Building on this model, we construct a {UCB} algorithm and establish new posterior concentration inequalities for the constrained posterior, leading to regret guarantees that are never worse than applying standard GP-{UCB} without concavity information and can be strictly tighter when concavity is informative. Experiments on benchmark problems and a Warfarin dosing test application demonstrate substantial reductions in cumulative regret relative to state-of-the-art baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/li26k.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26k/li26k.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26k.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kevin family: Li - given: Eric family: Laber editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3762-3784 id: li26k issued: date-parts: - 2026 - 8 - 6 firstpage: 3762 lastpage: 3784 published: 2026-08-06 00:00:00 +0000 - title: 'Probabilistic Verification of Neural Networks via Efficient Probabilistic Hull Generation' abstract: 'The problem of probabilistic verification of a neural network investigates the probability of satisfying the safe constraints in the output space when the input is given by a probability distribution. It is significant to answer this problem when the input is affected by disturbances which are often modeled by probabilistic variables. In the paper, we propose a novel neural network probabilistic verification framework which computes a guaranteed range for the safe probability by efficiently finding safe and unsafe probabilistic hulls. Our approach consists of three main innovations: (1) a state space subdivision strategy using regression trees to produce probabilistic hulls, (2) a boundary-aware sampling method which identifies the safety boundary in the input space using samples that are later used for building regression trees, and (3) iterative refinement with probabilistic prioritization for computing a guaranteed range for the safe probability. The accuracy and efficiency of our approach are evaluated on various benchmarks including ACAS Xu and a rocket lander controller. The result shows a clear improvement over the state of the art.' volume: 337 URL: https://proceedings.mlr.press/v337/li26l.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/li26l/li26l.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-li26l.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jingyang family: Li - given: Xin family: Chen - given: Hongfei family: Fu - given: Guoqiang family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3785-3801 id: li26l issued: date-parts: - 2026 - 8 - 6 firstpage: 3785 lastpage: 3801 published: 2026-08-06 00:00:00 +0000 - title: 'HHC: Hierarchical Hypergraph Communication for Multi-Agent Systems' abstract: 'Cooperative multi-agent reinforcement learning ({MARL}) faces significant coordination challenges due to partial observability. Although communication can mitigate these issues, traditional methods often overlook the fact that agents can simultaneously belong to multiple collaborative groups, playing diverse roles. This limitation hinders the effective integration of tactical and strategic information. To address this, we propose Hierarchical Hypergraph Communication (HHC). In HHC, agents are modeled via a tactical-level hypergraph that supports overlapping multi-group memberships, facilitating the extraction of fine-grained tactical features. Simultaneously, these tactical hyperedges serve as virtual nodes to integrate and communicate strategic intents within a strategic-level hypergraph. This dual-layered architecture empowers agents to align individual actions with global strategies through a hierarchical communication process, thereby enhancing decision-making capabilities. Extensive experiments demonstrate the effectiveness of HHC in complex coordination tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/liang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/liang26a/liang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-liang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Qifan family: Liang - given: Chenlong family: Li - given: Feiyu family: Wang - given: Jing family: Fu - given: Yixiang family: Shan - given: Lu family: Guo - given: Wei family: Liu - given: Lichang family: Song - given: Ting family: Long editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3802-3818 id: liang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3802 lastpage: 3818 published: 2026-08-06 00:00:00 +0000 - title: 'Grokked Models are Better Unlearners' abstract: '*Grokking*—delayed generalization that emerges well after a model has fit the training data—has been linked to robustness and representation quality. We ask whether this training regime also helps with *machine unlearning*, i.e., removing the influence of specified data without full retraining. We compare applying standard unlearning methods *before* versus *after* the grokking transition across vision (CNNs/ResNets on CIFAR, SVHN and {ImageNet}) and language (a transformer on a TOFU-style setup). Starting from grokked checkpoints consistently yields (i) more **efficient forgetting** (fewer updates to reach a target forget level), (ii) **less collateral damage** (smaller drops on retained and test performance), and (iii) **more stable updates** across seeds, relative to early-stopped counterparts under identical unlearning algorithms. Analyses of features and curvature further suggest that post-grokking models learn *more modular representations* with reduced gradient alignment between forget and retain subsets, which facilitates selective forgetting. Our results highlight **when** a model is trained (pre- vs. post-grokking) as an orthogonal lever to **how** unlearning is performed, providing a practical recipe to improve existing unlearning methods without altering their algorithms.' volume: 337 URL: https://proceedings.mlr.press/v337/liang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/liang26b/liang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-liang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuanbang family: Liang - given: Yang family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3819-3840 id: liang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 3819 lastpage: 3840 published: 2026-08-06 00:00:00 +0000 - title: 'Overcoming Dependent Censoring in the Evaluation of Survival Models' abstract: 'Dependent censoring occurs when the event time and censoring time are not conditionally independent given the observed covariates. This complicates survival model evaluation because widely used metrics, such as the Brier score, typically handle right-censoring using inverse probability of censoring weighting ({IPCW}). Unfortunately, {IPCW} is valid only when the estimated censoring distribution is independent of the event time. We propose a dependent Brier score based on an Archimedean copula and the Copula-Graphic estimator, and establish consistency and asymptotic normality of its margin-time estimator. To evaluate the metric, we introduce a semi-synthetic framework that creates realistic dependent censoring while preserving the original covariate structure and known event times. Across 12 datasets, the proposed metric reduces estimation error by 12-16% on average relative to {IPCW}. Source code is available at https://github.com/thecml/DependentEVAL' volume: 337 URL: https://proceedings.mlr.press/v337/lillelund26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lillelund26a/lillelund26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lillelund26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Christian Marius family: Lillelund - given: Shi-ang family: Qi - given: Russell family: Greiner editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3841-3866 id: lillelund26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3841 lastpage: 3866 published: 2026-08-06 00:00:00 +0000 - title: 'Gradient-Guided Reward Optimization for Inference-time Alignment' abstract: 'Ensuring the reliability of Large Language Models ({LLMs}) under distribution drift requires inference-time adaptation. While inference-time alignment methods such as Best-of-$N$ and rejection sampling are widely used, they frame the task as a sampling-intensive, reward-guided search, leading to two key limitations: their performance is bounded by the base model’s generation quality, and their reliance on imperfect reward models makes them vulnerable to reward hacking. To address these challenges, we introduce *Gradient-Guided Reward Optimization* (GGRO), a lightweight inference-time method that performs targeted, minimal intervention during decoding via gradient guidance. Specifically, GGRO monitors token-level entropy to identify high-uncertainty regions indicative of drift or misalignment. Upon detection, it responds by injecting nudging tokens, generated using gradient signals from an off-the-shelf reward model, to steer the generation trajectory rather than merely re-ranking samples. Experiments show that GGRO consistently improves inference-time alignment across safety, helpfulness, and reasoning benchmarks. It also increases coverage of high-quality responses and robustness to reward hacking, with minimal computational overhead. Code is available at https://github.com/lhk2004/GGRO.' volume: 337 URL: https://proceedings.mlr.press/v337/lin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lin26a/lin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hankun family: Lin - given: Ruqi family: Zhang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3867-3887 id: lin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3867 lastpage: 3887 published: 2026-08-06 00:00:00 +0000 - title: 'Constrained Random Forest for Domain-Generalizable Classification' abstract: 'Domain generalization is a critical challenge in machine learning, where models must generalize outside their training domain(s) to unseen test or deployment domains without retraining. Motivated by the principle of independent causal mechanisms, the notion of domain invariance provides a principled causality-inspired approach to domain generalization. In this context, we introduce a general domain-constrained supervised learning framework where the aim is to learn a representation of the input data that results in improved domain invariance and stability in the resulting prediction model. Adapting the framework to tree-based learning, we introduce the Constrained Random Forest that prioritizes stable predictive mechanisms, leading to improved generalization across diverse environments. Experiments on synthetic and real-world datasets show improved robustness over competing methods, even in settings where the underlying assumptions that enable domain-invariant learning in theory are violated.' volume: 337 URL: https://proceedings.mlr.press/v337/lingjaerde26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lingjaerde26a/lingjaerde26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lingjaerde26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Camilla family: Lingjærde - given: Geir Kjetil family: Sandve - given: Arnoldo family: Frigessi - given: Sylvia family: Richardson - given: Johan family: Pensar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3888-3921 id: lingjaerde26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3888 lastpage: 3921 published: 2026-08-06 00:00:00 +0000 - title: 'EagleConv: Bio-inspired Dual-Foveated Convolution for Robust Small Object Detection' abstract: 'Small object detection underpins wide-area vision tasks such as UAV and remote-sensing imagery. However, standard convolutions often exhibit low-pass smoothing behavior, which suppresses the sparse edge cues of tiny targets and may cause them to be overwhelmed by background clutter, leading to semantic information loss at the early stages of feature extraction. Inspired by the dual-fovea physiology of the eagle eye, we propose EagleConv, a bio-inspired operator that superimposes three {Gaussian} components into a center-excitation, surround-inhibition, peripheral-context response profile to selectively amplify small-object signals while attenuating noise. Architecturally, EagleConv adopts a sparse dual-pathway design that integrates partial-channel depthwise dual-foveated filtering, pointwise channel mixing, and adaptive residual gating, followed by anti-aliasing downsampling for robust dimensionality reduction. Experiments on three public benchmarks show that augmenting YOLOv11s with EagleConv delivers consistent and significant gains over multiple convolution-augmentation baselines, achieving state-of-the-art performance and confirming its transferability and generality as a plug-and-play module for wide-area small-object detection.' volume: 337 URL: https://proceedings.mlr.press/v337/liu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/liu26a/liu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-liu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jianwei family: Liu - given: Lifei family: Hao - given: Baoqi family: Huang - given: Bing family: Jia - given: Xuandong family: Zhao editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3922-3932 id: liu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3922 lastpage: 3932 published: 2026-08-06 00:00:00 +0000 - title: 'LENS: Latent Precision Inference in Multi-LLM Routing' abstract: 'Large language model ({LLM}) routing aims to select an appropriate model for each query under performance–cost trade-offs. A natural approach to improve adaptivity is to leverage interaction feedback to form behavioral signatures and continuously refine routing decisions as the environment changes. However, in realistic deployments, such feedback can have highly variable effective precision due to selective logging, imperfect evaluation signals, and temporal drift. As a result, behavioral signatures may be noisy or weakly informative, and treating them as uniformly precise can miscalibrate performance estimation and destabilize routing effectiveness. We propose the \textbf{L}atent pr\textbf{E}cisio\textbf{N} inference \textbf{S}ystem (\textbf{LENS}), a probabilistic routing framework that explicitly models the latent precision of interaction-derived signals. LENS formulates routing as posterior utility maximization under imprecise supervision, and marginalizes over latent precision to adaptively control how strongly behavioral signatures influence model selection. We instantiate LENS with an efficient variational inference procedure and evaluate it on multi-{LLM} routing benchmarks across diverse tasks and distribution shifts. Experimental results show that LENS consistently improves performance–cost trade-offs, with particularly strong gains under task and model shifts.' volume: 337 URL: https://proceedings.mlr.press/v337/liu26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/liu26b/liu26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-liu26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Juntao family: Liu - given: Lixing family: Yu - given: Kun family: Yue - given: Zhiwen family: Tang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3933-3956 id: liu26b issued: date-parts: - 2026 - 8 - 6 firstpage: 3933 lastpage: 3956 published: 2026-08-06 00:00:00 +0000 - title: 'Score-Regularized Joint Sampling with Importance Weights for Flow Matching' abstract: 'Flow matching models effectively represent complex distributions, yet estimating expectations of functions of their outputs remains challenging under limited sampling budgets. Independent sampling often yields high-variance estimates, especially when rare but high-impact outcomes dominate the expectation. We propose a non-IID sampling framework that jointly draws multiple samples to cover diverse, salient regions of a flow matching model’s generative distribution. To balance diversity and quality, we introduce a score-based regularization for the diversity mechanism (SR), which uses the score function, i.e., the gradient of the log probability, to ensure samples are pushed apart within high-density regions of the data manifold, mitigating off-manifold drift. To enable unbiased estimation when desired, we further develop an approach for importance weighting of non-IID flow samples by learning a residual velocity field that reproduces the marginal distribution of the non-IID samples and by evolving importance weights along trajectories. Empirically, our method produces diverse, high-quality samples and accurate importance-weight estimates and debiased expectation estimates, advancing the reliable characterization of flow matching model outputs.' volume: 337 URL: https://proceedings.mlr.press/v337/liu26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/liu26c/liu26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-liu26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xinshuang family: Liu - given: Runfa family: Li - given: Shaoxiu family: Wei - given: Truong family: Nguyen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3957-3978 id: liu26c issued: date-parts: - 2026 - 8 - 6 firstpage: 3957 lastpage: 3978 published: 2026-08-06 00:00:00 +0000 - title: 'When Can We Learn from Noisy Logical Data? Parameterized Complexity of Approximate Concept Fitting in Description Logics' abstract: 'SAT-based bounded fitting—searching for a smallest logical concept that correctly classifies all given examples—yields sample-efficient {PAC} learning for structured hypothesis classes such as description logic (DL) concepts. Yet this paradigm is fundamentally brittle: it demands realizability, and a single mislabeled example can render the underlying SAT instance unsatisfiable. While agnostic learnability follows from finite VC-dimension of bounded-size concept classes, the real barrier is computational: minimizing misclassifications over all concepts of bounded size is NP-hard. We study this barrier through parameterized complexity. We introduce ApxFit(k,t)—the problem of deciding whether there exists a DL concept of size at most $k$ that misclassifies at most $t$ out of $m$ examples—and establish a complexity landscape for fragments of $\mathcal{ALC}$ whose operator sets contain $\{\sqcap,\exists\}$ or $\{\sqcup,\forall\}$: the problem is W[2]-hard parameterized by concept size $k$ (even for $t{=}0$), yet lies in XP parameterized by outlier count $t$ for any fixed $k$. Algorithmically, we lift bounded fitting from SAT to partial weighted MAX-SAT and combine it with structural risk minimization, yielding the first noise-tolerant DL concept learner with formal agnostic generalization guarantees.' volume: 337 URL: https://proceedings.mlr.press/v337/lu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lu26a/lu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Chang family: Lu - given: Yizheng family: Zhao - given: Renate family: Schmidt editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3979-3998 id: lu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 3979 lastpage: 3998 published: 2026-08-06 00:00:00 +0000 - title: 'Conformal Prediction Sets for Instance Segmentation' abstract: 'Current instance segmentation models achieve high performance on average predictions, but lack principled uncertainty quantification: their outputs are not calibrated, and there is no guarantee that a predicted mask is close to the ground truth. To address this limitation, we introduce a conformal prediction algorithm to generate adaptive confidence sets for instance segmentation. Given an image and a pixel coordinate query, our algorithm generates a confidence set of instance predictions for that pixel, with a provable guarantee for the probability that at least one of the predictions has high Intersection-Over-Union (IoU) with the true object instance mask. We apply our algorithm to instance segmentation examples in agricultural field delineation, cell segmentation, and vehicle detection. Empirically, we find that our prediction sets vary in size based on query difficulty and attain the target coverage, outperforming baselines (naive best parameter and morphological dilation-based methods). We provide versions of the algorithm with asymptotic and finite sample guarantees. Our work is the first to capture structural uncertainty in instance segmentation by constructing confidence sets of diverse segmentation predictions.' volume: 337 URL: https://proceedings.mlr.press/v337/lu26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lu26b/lu26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lu26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kerri family: Lu - given: Dan M. family: Kluger - given: Stephen family: Bates - given: Sherrie family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 3999-4026 id: lu26b issued: date-parts: - 2026 - 8 - 6 firstpage: 3999 lastpage: 4026 published: 2026-08-06 00:00:00 +0000 - title: 'Computing Exact Nash Equilibria in Graphical Games: A Geometric Approach to Paths, Stars, and Caterpillars' abstract: 'Computing mixed-strategy {Nash} equilibria (MSNE) in graphical games being PPAD-complete, special types of graphical games have received a lot of attention over the years. We present a number of new results using a geometric approach to computing exact MSNE. We consider graphical games of several structures, such as paths, stars, and caterpillars. We also consider graphical polymatrix games on these structures. We provide a new tight upper bounding result for path-structured graphical games and a new quadratic-time algorithm for representing all MSNE and computing one for path-structured polymatrix games. For star graphical games, our algorithm is logarithmic time for non-degenerate cases (i.e., without symmetric players) and linear time for general cases with symmetric players. Interestingly, having more symmetric players makes the computation more expensive. For star polymatrix games, our algorithm is linear in the input size. For the open problems on caterpillar polymatrix and graphical games, our algorithms are polynomial time in the input size.' volume: 337 URL: https://proceedings.mlr.press/v337/lucca26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lucca26a/lucca26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lucca26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Evan family: Lucca - given: Mohammad T. family: Irfan - given: Luis E. family: Ortiz editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4027-4066 id: lucca26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4027 lastpage: 4066 published: 2026-08-06 00:00:00 +0000 - title: 'The relative value of interventional and observational samples in Bayesian Causal Linear Gaussian Models' abstract: 'We investigate the asymptotic properties of {Bayesian} bivariate causal discovery for {Gaussian} Linear Structural Equation Models ({SEMs}) with heteroscedastic noise. We demonstrate that with purely observational data, the posterior distribution over the models fails to consistently identify the true causal structure—a consequence of the fundamental non-identifiability within the {Markov} Equivalence Class. Specifically, if the true generating mechanism corresponds to a connected graph ($A \rightarrow B$ or $B \rightarrow A$), the asymptotic behavior of the posterior is given by the ratio between the prior on the true model and the push-forward prior of the alternative. In contrast, for the independence model, we establish that the posterior concentrates at a stochastic polynomial rate of $O_p(n^{-1/2})$. To resolve this non-identifiability, we incorporate $m$ interventional samples and characterize the concentration rates as a function of the observational-to-total sample ratio, $\eta$. We identify a sharp \textit{concentration dichotomy}: while the independence graph maintains a polynomial $O_p(N^{-1/2})$ rate (where $N = n+m$), connected graphs undergo a phase transition to exponentially fast convergence. This highlights an \textit{exponential} relative importance between the two data types, as altering the amount of one data type directly changes the exponent governing the concentration speed. We derive explicit formulae for the exponential decay rates and provide precise conditions under which mixing observational and interventional data optimizes concentration speed. Finally, our theoretical findings are validated through empirical simulations in {Bayesian} {Gaussian} equivalent (BGe)-style prior specifications offering a principled foundation for experimental design in {Bayesian} causal discovery.' volume: 337 URL: https://proceedings.mlr.press/v337/lungu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/lungu26a/lungu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-lungu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Valentinian Mihai family: Lungu - given: Anish family: Dhir - given: Mark prefix: van der family: Wilk - given: Ioannis family: Kontoyiannis editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4067-4099 id: lungu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4067 lastpage: 4099 published: 2026-08-06 00:00:00 +0000 - title: 'First-Order Softmax Weighted Switching Gradient Method for Distributed Stochastic Minimax Optimization with Stochastic Constraints' abstract: 'This paper addresses the distributed stochastic minimax optimization problem subject to stochastic constraints. We propose a novel first-order Softmax-Weighted Switching Gradient method tailored for federated learning. Under full client participation, our algorithm achieves the standard $\tilde{\mathcal{O}}(\epsilon^{-4})$ oracle complexity to satisfy a unified bound $\epsilon$ for both the optimality gap and feasibility tolerance. We extend our theoretical analysis to the practical partial participation regime by quantifying client sampling noise through a stochastic superiority assumption. Furthermore, by relaxing standard boundedness assumptions on the objective functions, we establish a strictly tighter lower bound for the softmax hyperparameter. We provide a unified error decomposition and establish a sharp $\mathcal{O}(\log\frac{1}{\delta})$ high-probability convergence guarantee. Ultimately, our framework demonstrates that a single-loop primal-only switching mechanism provides a stable alternative for optimizing worst-case client performance, effectively bypassing the hyperparameter sensitivity and convergence oscillations often encountered in traditional primal-dual or penalty-based approaches. We verify the efficacy of our algorithm via experiment on the Neyman-Pearson (NP) classification, fair classification, and federated safe reinforcement learning tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/luo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/luo26a/luo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-luo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhankun family: Luo - given: Antesh family: Upadhyay - given: Sang Bin family: Moon - given: Abolfazl family: Hashemi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4100-4155 id: luo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4100 lastpage: 4155 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Expressive Random Feature Models via Parametrized Activations' abstract: 'The random feature (RF) method is a powerful kernel approximation technique, but it typically uses fixed activation functions, limiting its adaptability across diverse tasks. To overcome this limitation, we introduce the Random Feature Model with Learnable Activation Functions (RFLAF), a novel statistical model that parameterizes activation functions as weighted sums of basis functions within the random feature framework. Examples of basis functions include radial basis functions (RBFs), spline functions, polynomials, and so forth. For theoretical results, we consider RBFs as representative basis functions. We start with a single RBF as the activation, and then extend the results to multiple RBFs, demonstrating that RF models with a learnable activation component substantially expand the represented function space. We provide estimates on the required number of samples and random features to achieve low excess risk. In our experiments, we test RFLAF with three types of bases: radial basis functions, spline functions and polynomials. Experimental results show that RFLAFs with RBFs and splines consistently outperform other RF models, where RBFs are three times more computationally efficient than splines. We then unfreeze the first-layer parameters and retrain the models, validating the expressivity advantage of learnable activation components on regular two-layer neural networks. Our work provides a deeper understanding of learnable activation components within modern neural network architectures.' volume: 337 URL: https://proceedings.mlr.press/v337/ma26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ma26a/ma26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ma26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zailin family: Ma - given: Jiansheng family: Yang - given: Yaodong family: Yang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4156-4204 id: ma26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4156 lastpage: 4204 published: 2026-08-06 00:00:00 +0000 - title: 'Bayesian Causal Discovery in Directed Cyclic Graphs with Closed-Form Lag Bayes Factors' abstract: 'In coarsely sampled longitudinal data, feedback loops can appear as cyclic contemporaneous structure, yet most causal-discovery methods assume acyclicity. {Bayesian} directed cyclic graph models allow cycles by using non-{Gaussian} errors with lagged outcomes and exogenous covariates to identify contemporaneous structure. However, consecutive lags are often highly correlated. Existing methods place a binary indicator on each candidate lag, creating exponentially many lag patterns per edge; evidence for a true edge can split across correlated configurations and fall below selection thresholds (posterior fragmentation). We replace these indicators with one categorical variable recording edge absence or active lag, so lags compete within one state space. Under the {Gaussian} scale-mixture of {Laplace} errors, each candidate coefficient integrates out exactly, yielding closed-form {Bayes} factors from cached scalars with no matrix operations for lag comparison. We prove edge-and-lag selection consistency and show that the at-most-one-active-lag assumption is least costly where fragmentation is most severe; the method is a finite-sample regulariser for correlated-lag regimes, not a uniformly better alternative. Cached sufficient statistics and incremental Cholesky updates make the sampler 55–67 times faster without changing the target posterior. In the largest single-lag synthetic benchmark, the categorical encoding raises the true-positive rate from 0.83 to 0.99 and lowers structural Hamming distance from 6.0 to 0.3. On the Health and Retirement Study panel (17,883 individuals, 13 waves), both formulations share a four-edge contemporaneous core, but the categorical encoding yields larger autoregressive coefficients and a sparser contemporaneous graph than the independent encoding.' volume: 337 URL: https://proceedings.mlr.press/v337/maadi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/maadi26a/maadi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-maadi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Seyed Reza family: Maadi - given: Sally family: Cripps editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4205-4231 id: maadi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4205 lastpage: 4231 published: 2026-08-06 00:00:00 +0000 - title: 'Approximating Nash Equilibria in Finite-Horizon Multi-Adversarial Team Markov Games' abstract: 'Multi-Adversarial Team Games (MATGs) extend the canonical normal-form framework of von Stengel and Koller – where a team of players sharing a common objective but unable to coordinate faces a single adversary - to settings involving multiple independent adversaries. From an algorithmic perspective, MATGs are notable as one of the few game classes admitting polynomial-time algorithms for computing $\varepsilon$-{Nash} equilibria. However, no complexity or algorithmic guarantees are known for the finite-horizon Markovian generalisation of MATGs. This paper establishes positive and negative results for approximating \emph{non-stationary} {Nash} equilibria in finite-horizon Multi-Adversarial Team {Markov} Games. Specifically, we provide a polynomial-time algorithm for the single-adversary case, prove PPAD-hardness for the multiple-adversary case and present a polynomial-time algorithm for the multiple-adversary setting with additive transitions. We also provide an empirical evaluation of the proposed algorithms.' volume: 337 URL: https://proceedings.mlr.press/v337/maddila26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/maddila26a/maddila26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-maddila26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Prasanna family: Maddila - given: Régis family: Sabbadin - given: Meritxell family: Vinyals editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4232-4251 id: maddila26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4232 lastpage: 4251 published: 2026-08-06 00:00:00 +0000 - title: 'Information-Theoretic Lower Bounds for Causal Inference under Credal Uncertainty' abstract: 'Causal effect estimation from observational data typically assumes a single fixed observational distribution. We study the setting in which the distribution is known only to belong to a credal set, a convex set of plausible observational laws. Our results characterize how this observational ambiguity is transformed by causal identification formulas. First, using standard two-point information-theoretic tools after composition with the interventional map, we derive lower bounds for causal effect estimation. The key message is a causal amplification phenomenon: observational discrepancies in low-propensity treatment strata can be hard to detect while producing separated interventional effects. Consequently, in the binary hard-pair constructions, sample complexity scales as $\Omega(1/(\pi_0\varepsilon^2))$ or $\Omega(1/(\beta_0\varepsilon^2))$, and the average treatment effect need not incur an additional dependence on the number of strata. Second, we prove Lipschitz bounds for the interventional mapping, with amplification factor $(1+1/\alpha_{\min})$, showing how positivity controls robust identification width. Third, we study minimax regret for causal decisions under credal uncertainty and show that randomization can halve worst-case regret in a symmetric action-separation construction. We also give matching upper bounds in special cases and an NP-hardness result for computing robust identification width. The experiments are diagnostic checks of the tight hard-instance scaling laws rather than broad empirical benchmarks.' volume: 337 URL: https://proceedings.mlr.press/v337/mai26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mai26a/mai26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mai26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hung family: Mai - given: Hai family: Nguyen - given: Khanh family: Nguyen - given: Luong family: Doan - given: Nhung family: Duong - given: Phong family: Ho - given: Tuan family: Do editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4252-4271 id: mai26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4252 lastpage: 4271 published: 2026-08-06 00:00:00 +0000 - title: 'Learning plug-in surrogate endpoints for randomized experiments' abstract: 'Surrogate endpoints are used in place of long-term outcomes in randomized experiments when observing the real outcome for a large enough cohort is prohibitively expensive or impractical. A short-term surrogate is good if the result of an experiment using the surrogate is predictive of the result of a hypothetical study using the real outcome. Much attention has been paid to formalizing this property in causal terms, but most criteria are unidentifiable and cannot be turned into practical algorithms for learning surrogate endpoints from data. To address this, we study plug-in composite surrogates, functions of post-treatment variables that may be substituted directly for the primary outcome in a randomized experiment. We propose two methods for learning plug-in surrogates that maximize effect predictiveness, and characterize the possibility of finding endpoints that yield unbiased effect estimates in representative scenarios. Finally, in both synthetic experiments with known effects and in data from a real-world experiment, we find that our method, based on directly modeling the surrogate effect, returns plug-in endpoints more predictive of the primary effect than established methods.' volume: 337 URL: https://proceedings.mlr.press/v337/margueritte26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/margueritte26a/margueritte26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-margueritte26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Alessandro-Umberto family: Margueritte - given: Ahmet Zahid family: Balcıoğlu - given: Jesse H. family: Krijthe - given: Dave family: Zachariah - given: Fredrik D. family: Johansson editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4272-4298 id: margueritte26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4272 lastpage: 4298 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Latent Energy-Based Models via Interacting Particle Langevin Dynamics' abstract: 'We develop interacting particle algorithms for learning latent variable models with energy-based priors. To do so, we leverage recent developments in particle-based methods for solving maximum marginal likelihood estimation (MMLE) problems. Specifically, we provide a continuous-time framework for learning latent energy-based models, by defining stochastic differential equations (SDEs) that provably solve the MMLE problem. We obtain a practical algorithm as a discretisation of these SDEs and provide theoretical guarantees for the convergence of the proposed algorithm. Finally, we demonstrate the empirical effectiveness of our method on synthetic and image datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/marks26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/marks26a/marks26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-marks26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Joanna family: Marks - given: Tim Y. J. family: Wang - given: Omer Deniz family: Akyildiz editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4299-4322 id: marks26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4299 lastpage: 4322 published: 2026-08-06 00:00:00 +0000 - title: 'cc-Shapley: Measuring Multivariate Feature Importance Needs Causal Context' abstract: 'Explainable artificial intelligence promises to yield insights into relevant features, thereby enabling humans to examine and scrutinize machine learning models or even facilitating scientific discovery. Considering the widespread technique of {Shapley} values, we find that purely data-driven operationalization of multivariate feature importance is unsuitable for such purposes. Even for simple problems with two features, spurious associations due to collider bias and suppression arise from considering one feature only in the observational context of the other, which can lead to misinterpretations. Causal knowledge about the data-generating process is required to identify and correct such misleading feature attributions. We propose cc-{Shapley} (causal context {Shapley}), an interventional modification of conventional observational {Shapley} values leveraging knowledge of the data’s causal structure, thereby analyzing the relevance of a feature in the causal context of the remaining features. We show theoretically that this eradicates spurious association induced by collider bias. We compare the behavior of {Shapley} and cc-{Shapley} values on various, synthetic, and real-world datasets. We observe nullification or reversal of associations when moving from observational to cc-{Shapley}.' volume: 337 URL: https://proceedings.mlr.press/v337/martin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/martin26a/martin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-martin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jörg family: Martin - given: Stefan family: Haufe editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4323-4352 id: martin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4323 lastpage: 4352 published: 2026-08-06 00:00:00 +0000 - title: 'AudiFair: Privacy-Preserving Framework for Auditing Fairness' abstract: 'Ensuring fairness in {AI} is challenging, especially when privacy concerns prevent access to proprietary models and training data. We propose a cryptographic framework for auditing fairness without requiring model disclosure. Unlike existing solutions – which either fail to capture attack vectors enabling dishonest model providers to pass audits unfairly, or require continuous auditing during deployment involving real-world users – our framework is the first to simultaneously achieve the following: $\textbf{(1) Model Privacy}$: Proprietary model details remain hidden from verifiers; $\textbf{(2)}$ A dishonest model provider cannot cause a non-compliant model to pass the fairness audit without detection by the verifier; $\textbf{(3) Pre-deployment Certification}$: The certification can be conducted entirely prior to deployment, without requiring interaction with or data from real-world users; $\textbf{(4) Test Data Transparency}$: Test data for auditing is generated in a transparent and accountable way, preventing dishonest parties from manipulating it. We achieve these goals by carefully combining cryptographic commitments, coin tossing, and zero-knowledge proofs. We evaluate our protocol on decision trees, XGBoost, and neural networks. Our results confirm the practicality of our approach: for a dataset with 10,000 samples and 10 features, and an XGBoost model with 100 trees of depth 3, proof generation takes 42 seconds and verification takes 2 seconds.' volume: 337 URL: https://proceedings.mlr.press/v337/masserova26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/masserova26a/masserova26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-masserova26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Elisaweta family: Masserova - given: Kshitij family: Kulkarni - given: Antigoni family: Polychroniadou - given: Ron D. family: Rothblum - given: Akira family: Takahashi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4353-4380 id: masserova26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4353 lastpage: 4380 published: 2026-08-06 00:00:00 +0000 - title: 'Provable Guarantees For Robust Feature Selection in Sparse Linear Models in High-Dimensions' abstract: 'We study feature selection (support recovery) in sparse linear models, including linear and logistic regression, under a strong adversarial contamination model where an adversary can arbitrarily corrupt a constant fraction of samples in the high-dimensional regime. Most of the existing methods target one or two aspects of this interesting problem: (1) achieving robustness against \emph{strong} adversaries, (2) handling adversarial corruption in \emph{both} features and labels, and (3) performing feature selection in \emph{high dimensions}. Our approach tackles all three issues simultaneously. We propose a trimmed maximum likelihood estimator with $\ell_1$-regularization, leading to a non-convex relaxation of an NP-hard combinatorial optimization problem. We prove that any locally optimal solution to this non-convex problem achieves \emph{near-minimax} optimal statistical rates, up to logarithmic factors. Critically, our method recovers the true support in a computationally efficient manner despite the intractability of the exact formulation. The resulting sample complexity scales only logarithmically with the ambient dimension, making it well-suited for high-dimensional settings. Furthermore, our framework accommodates heavy-tailed noise distributions under mild moment assumptions, requiring only that the fourth moment be bounded. We also validate our theoretical findings empirically.' volume: 337 URL: https://proceedings.mlr.press/v337/maurya26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/maurya26a/maurya26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-maurya26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Deepak family: Maurya - given: Adarsh family: Barik - given: Jean family: Honorio editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4381-4426 id: maurya26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4381 lastpage: 4426 published: 2026-08-06 00:00:00 +0000 - title: 'Meta-Dependence in Conditional Independence Testing' abstract: 'Conditional independence testing is a critical component of feature screening, invariant statistical models, and causal discovery. Many of these algorithms rely on the sequential application of conditional independence tests, and their stability hinges on how their outcomes interact. We study this "meta-dependence" between conditional independence properties using the following geometric intuition: satisfying each conditional independence property constrains the space of possible joint distributions to a manifold. The "meta-dependence" of multiple conditional independences in a probability distribution is informed by its position relative to these manifolds. We provide a simple-to-compute measure of this meta-dependence using moment projections, with a closed-form expression for multivariate {Gaussian} distributions, and consolidate our findings empirically using both synthetic and real-world data. Our measure of meta-dependence does not rely on graphical properties of the distribution and can be computed directly from summary statistics such as a covariance matrix, allowing for various applications. We demonstrate one use case of meta-dependence, using a simple redundancy metric to tune significance thresholds and improve causal discovery.' volume: 337 URL: https://proceedings.mlr.press/v337/mazaheri26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mazaheri26a/mazaheri26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mazaheri26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bijan family: Mazaheri - given: Jiaqi family: Zhang - given: Caroline family: Uhler editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4427-4440 id: mazaheri26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4427 lastpage: 4440 published: 2026-08-06 00:00:00 +0000 - title: 'Relaxing Faithfulness with Intervention-Only Causal Discovery' abstract: 'Causal discovery algorithms learn a network that describes the causal dependencies among random variables. A common workflow involves first utilizing conditional independence properties on observational data to determine partially directed causal relationships, then applying interventions to orient the unknown causal directions. A critical assumption for the first step is faithfulness: a requirement that causally linked variables exhibit statistical dependence. Many natural systems include buffering and stabilizing pathways that cancel out to achieve systemic robustness. This cancellation of pathways violates faithfulness, leading causal discovery algorithms to incorrectly remove causal dependencies. In this paper, we argue that hard interventions contain information about the presence/absence of causal linkage that is overlooked in the first stage of structure discovery. We show that a mild assumption — called intervention-immediacy faithfulness — that allows cancellations, is sufficient to nonparametrically identify causal structures with hard interventions. These results position interventions as the primary carriers of information about causal structure, which should take precedence over conditional independence testing. To flip the paradigm, we also specify equivalence classes when the identification criteria are not met due to limitations in the scope of interventions.' volume: 337 URL: https://proceedings.mlr.press/v337/mazaheri26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mazaheri26b/mazaheri26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mazaheri26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bijan family: Mazaheri - given: Jiaqi family: Zhang - given: Caroline family: Uhler editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4441-4456 id: mazaheri26b issued: date-parts: - 2026 - 8 - 6 firstpage: 4441 lastpage: 4456 published: 2026-08-06 00:00:00 +0000 - title: 'Causal Discovery in Mixtures of Populations' abstract: 'Causal discovery aims to learn causal structures up to certain symmetries. Diverse populations or changing environments give rise to heterogeneous data in the following sense: each population/environment is a “source” which idiosyncratically determines the forms of causal effects. From this perspective, the source is a latent common cause for every observed variable. While some methods for causal discovery can work around latent confounding in special cases, a global confounder poses a significant challenge. The only known ways to deal with latent global confounding involve making assumptions that limit structural equations and/or noise functions. We demonstrate that globally confounded causal structures can still be identified with arbitrary structural equations and noise functions, so long as the number of latent classes remains small relative to the size and sparsity of the underlying {DAG}. The approach relies on agglomerating variables into large-enough matrices of moments, whose ranks directly reveal graphical properties of the causal structure. We also provide a statistical test to test the rank of these matrices.' volume: 337 URL: https://proceedings.mlr.press/v337/mazaheri26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mazaheri26c/mazaheri26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mazaheri26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bijan family: Mazaheri - given: Spencer L. family: Gordon - given: Yuval family: Rabani - given: Leonard family: Schulman editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4457-4478 id: mazaheri26c issued: date-parts: - 2026 - 8 - 6 firstpage: 4457 lastpage: 4478 published: 2026-08-06 00:00:00 +0000 - title: 'Conformal Graph Prediction with Z-Gromov Wasserstein Distances' abstract: 'Supervised graph prediction addresses regression problems where the outputs are structured graphs. Although several approaches exist for graph-valued prediction, principled uncertainty quantification remains limited. We propose a conformal prediction framework for graph-valued outputs, providing distribution-free coverage guarantees in structured output spaces. Our method defines nonconformity via the {Z-Gromov}–{Wasserstein} distance, instantiated in practice through Fused Gromov–{Wasserstein} (FGW), enabling permutation-invariant comparison between predicted and candidate graphs. To obtain adaptive prediction sets, we introduce Score Conformalized Quantile Regression (SCQR), an extension of Conformalized Quantile Regression (CQR) to handle complex output spaces such as graph-valued outputs. We evaluate the proposed approach on a synthetic task and a real problem of molecule identification.' volume: 337 URL: https://proceedings.mlr.press/v337/melo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/melo26a/melo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-melo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Gabriel family: Melo - given: Thibaut prefix: de family: Saivre - given: Anna family: Calissano - given: Florence family: d’Alché-Buc editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4479-4496 id: melo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4479 lastpage: 4496 published: 2026-08-06 00:00:00 +0000 - title: 'Exact Uncertainty Propagation via Gaussian Process Neurons' abstract: 'Exact marginalization in deep {Gaussian} processes (DGPs) is analytically intractable, typically requiring computationally costly sampling-based approximations. We introduce the {Gaussian} process neuron, a computational unit built on a novel {Wasserstein} exponential kernel. By defining a composable map between factorized {Gaussian} measures, this unit enables analytical uncertainty propagation; concurrently, optimizing deterministic inducing variables via maximum a posteriori estimation ensures strict probabilistic rigor. By eliminating sampling variance and the depth-scaling computational bottlenecks of Monte Carlo methods, our approach enables exact probabilistic variants of diverse architectures, including DGPs, multilayer perceptrons, and {Kolmogorov}-Arnold Networks. Empirically, these networks demonstrate superior uncertainty calibration relative to state-of-the-art approximate {DGP} frameworks, alongside high-dimensional scalability and robust compositional expressiveness.' volume: 337 URL: https://proceedings.mlr.press/v337/meng26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/meng26a/meng26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-meng26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Qiuxian family: Meng - given: Yongyou family: Zhang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4497-4513 id: meng26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4497 lastpage: 4513 published: 2026-08-06 00:00:00 +0000 - title: 'Globally Optimal Multi-Object Tracking with Splitting and Merging' abstract: 'In multi-object tracking (MOT), the trajectories of moving objects – e.g., molecules, cells, or people – must be recovered from detected positions. MOT is often solved using network flow approaches to find globally optimal solutions. Here, we consider a version of MOT where objects can split or merge – such as cells that are moving but also dividing while being tracked. We show that this problem is NP-hard, phrase it as a Max-SAT problem, and ask: (1) To what extent can modern optimized satisfiability solvers be applied to realistic MOT problems? (2) Are the globally optimal solutions better than those generated by existing methods? Using both simulated data and real-world cell tracking data, we show that Max-SAT is a computationally costly but feasible approach that can lead to substantially improved solutions for problems of realistic size. We hope that the Max-SAT instances generated by the MOT problem can serve as practically relevant benchmarking cases for the future improvement of Max-SAT solvers.' volume: 337 URL: https://proceedings.mlr.press/v337/mihaylova26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mihaylova26a/mihaylova26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mihaylova26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mihaela family: Mihaylova - given: Jelle family: Piepenbrock - given: Johannes family: Textor editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4514-4527 id: mihaylova26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4514 lastpage: 4527 published: 2026-08-06 00:00:00 +0000 - title: 'Robust estimation of graphical models with measurement error: False discovery control and sensitivity analysis' abstract: 'This paper addresses the problem of learning {Gaussian} graphical models from data contaminated by additive measurement error. Applying traditional procedures to the noisy data may result in many false discoveries. On the other hand, existing procedures that explicitly account for measurement error assume that the measurement error covariance is known or can be estimated precisely. We provide two practical alternatives for the common setting where this side information is not available. The first proposed method follows a partial identification approach and estimates a graph with controlled false discovery rate when given an upper bound on the measurement error variances. In many settings, the precise variance of the errors is unknown, but the scientist may still confidently specify an upper bound. The second framework is a sensitivity analysis that assesses the minimum amount of measurement error required to explain away an estimated edge. This yields an interpretable measure for practitioners to assess which estimated edges are robust and which may be simply due to measurement error. We derive theoretical guarantees and show good empirical performance in simulations. We further illustrate the practical utility of our procedures on a single-cell mRNA sequencing dataset.' volume: 337 URL: https://proceedings.mlr.press/v337/mingelgrin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mingelgrin26a/mingelgrin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mingelgrin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shira family: Mingelgrin - given: Y. Samuel family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4528-4542 id: mingelgrin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4528 lastpage: 4542 published: 2026-08-06 00:00:00 +0000 - title: 'Long term sequential decision making under risk' abstract: 'We study finite-horizon {MDP} planning under \emph{root-based} (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns. Such objectives are non-linear in the return distribution and generally break {Bellman} optimality, so direct optimization by scenario-tree enumeration is intractable. We propose \textbf{ERQDP}, an enumeration-free and sampling-free method that solves a rank–quantile surrogate via exact {DP} (Dynamic Programming), evaluates candidate policies exactly by {DP} over return Probability Mass Functions (PMFs) on a discretized return grid (with an explicit rounding bound), and refines the surrogate in an anytime loop that reports an explicit upper–lower gap (certificate) for the target objective up to discretization budgets. Across tested benchmarks, ERQDP returns certified solutions or explicit residual gaps, enables fast risk-parameter sweeps with substantial runtime gains, and supports both risk-averse and risk-seeking behaviors.' volume: 337 URL: https://proceedings.mlr.press/v337/mirzanejad26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mirzanejad26a/mirzanejad26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mirzanejad26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mohammad family: Mirzanejad - given: Nadjet family: Bourdache - given: Abdel-illah family: Mouaddib editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4543-4560 id: mirzanejad26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4543 lastpage: 4560 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Stable Digraphs from Sparse-Input Linear Structural Causal Models' abstract: 'We propose StableSpIn, a continuous optimization framework for learning potentially cyclic causal directed graphs (digraphs) in linear structural equation models via a spectral-radius constraint on the absolute adjacency matrix. Our motivation is twofold: first, stability is a natural requirement for linear structural models; second, the contractive cycles that stability induces facilitate the identifiability of digraphs. We formulate causal discovery as a likelihood-based optimization problem under a sparse-input assumption, yielding a scalable algorithm applicable to both cross-sectional and time-series data. Unlike prior continuous acyclicity constraints, our stability regularizer is cheaper to evaluate while accommodating general digraphs, yielding faster optimization in practice. Experiments on synthetic benchmarks show improved graph recovery over state-of-the-art baselines, and empirical studies on U.S., European, and Swiss equity markets reveal interpretable cyclic dependencies that persist across time windows. Our implementation is available at https://github.com/pmisiakos/StableSpIn.' volume: 337 URL: https://proceedings.mlr.press/v337/misiakos26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/misiakos26a/misiakos26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-misiakos26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Panagiotis family: Misiakos - given: Markus family: Püschel editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4561-4594 id: misiakos26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4561 lastpage: 4594 published: 2026-08-06 00:00:00 +0000 - title: 'Wasserstein Gradient Flows for Scalable and Regularized Barycenter Computation' abstract: '{Wasserstein} barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not because as they assume access to the complete set of samples from the input measures. Meanwhile, neural network approaches do scale well, but rely on complex optimization problems and cannot easily incorporate label information. We address these limitations through gradient flows in the space of probability measures. Through time discretization, we achieve a scalable algorithm that i) relies on mini-batch optimal transport, ii) accepts modular regularization through task-aware functions, and iii) seamlessly integrates supervised information into the ground-cost. We empirically validate our approach on domain adaptation benchmarks that span computer vision, neuroscience, and chemical engineering. Our method establishes a new state-of-the-art {Wasserstein} barycenter solver, with labeled barycenters consistently outperforming unlabeled ones. Our code at https://github.com/SigmaNova/barycentric-gradient-flows' volume: 337 URL: https://proceedings.mlr.press/v337/fernandes-montesuma26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/fernandes-montesuma26a/fernandes-montesuma26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-fernandes-montesuma26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Eduardo family: Fernandes Montesuma - given: Yassir family: Bendou - given: Mike family: Gartrell editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4595-4606 id: fernandes-montesuma26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4595 lastpage: 4606 published: 2026-08-06 00:00:00 +0000 - title: 'Causal Reasoning with Bipartite Graphical Causal Models' abstract: 'Causal {Bayesian} networks (CBNs) and structural causal models (SCMs) are the dominant frameworks for graphical causal reasoning, but they cannot adequately represent all real-world causal systems. In particular, systems at equilibrium—where feedback mechanisms create cyclic causal dependencies—can exhibit causal semantics that are fundamentally incompatible with these frameworks: different interventions that enforce the same variable value may have different effects, rendering the standard “perfect intervention” $\mathrm{do}(X=x)$ ambiguous. We propose _bipartite graphical causal models_ (BGCMs), in which the structure of a system of equations is encoded by a bipartite graph with variable and equation nodes. In this framework, a hard intervention $\mathrm{do}(f_j : X_v=\xi_v)$ specifies which equation is replaced, which variable is targeted, and at what value—resolving the ambiguity of the standard notion. We demonstrate, through a detailed case study of a physical system, that this representation naturally corresponds to distinct real-world interventions. We formulate a {Markov} property in terms of a new graphical separation criterion ($B$-separation) that exploits the functional determinism inherent in the equations, and we extend it to settings with non-random inputs. We show how this gives rise to a do-calculus for reasoning about domain invariances. BGCMs strictly generalize CBNs and SCMs while retaining the ability to perform graphical causal reasoning.' volume: 337 URL: https://proceedings.mlr.press/v337/mooij26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mooij26a/mooij26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mooij26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Joris M. family: Mooij editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4607-4633 id: mooij26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4607 lastpage: 4633 published: 2026-08-06 00:00:00 +0000 - title: 'Learning to Infer Fast by Attending to Sparse Temporal Observations' abstract: 'Many scientific datasets contain sparse, irregular observations of dynamic processes. Fast inference techniques are required to infer the unseen evolution of physical systems underlying growing datasets, and estimate the parameters that govern them. We first accelerate the convergence of Gauss-{Markov} Variational Inference via efficient natural gradient computation and automatic step-size adaptation. We then propose two general-purpose schemes for initialization from sparse data, one using junction tree representations of Gauss-{Markov} distributions, and another attention-based neural network architecture that learns to predict correlated temporal posteriors. We show that these initializers dramatically improve performance for ecological models of soil decomposition and predator-prey dynamics. We further extend our methods to a semiparametric epidemiological model of SARS-CoV-2 RNA wastewater measurements, which uses {Gaussian} processes to model uncertainty in latent reproduction numbers. Our methods allow for quick inference of both local states and global dynamical parameters, and unlike prior work, can be applied even when measurements are sparse and the generative process is not fully known.' volume: 337 URL: https://proceedings.mlr.press/v337/motamed26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/motamed26a/motamed26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-motamed26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mehrnaz family: Motamed - given: Harry family: Bendekgey - given: Debora family: Sujono - given: Erik B. family: Sudderth editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4634-4660 id: motamed26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4634 lastpage: 4660 published: 2026-08-06 00:00:00 +0000 - title: 'Model Agnostic Graph Prompt Learning for Crystal Property Prediction' abstract: 'Graph Neural Networks have emerged as a powerful tool for the fast and accurate prediction of various crystal properties. These models often encode domain-specific knowledge into their graph encoding modules, which increases their parameter size and makes their performance heavily dependent on domain expertise. Added to this, explicitly incorporating all chemical and structural features, that might influence a specific crystal property into the GNN encoder, is a challenging task. In this work, we propose a soft prompt learning framework that captures latent features essential for property prediction, which are not explicitly provided to the GNN. We introduce a novel multilevel graph prompt learning framework comprising both node-level and graph-level soft prompts. At the node level, we capture the local chemical semantics of different atom types, while at the graph level, we encode the global structural symmetry of the crystal graph. Our proposed prompt learning framework is lightweight and seamlessly integrates with any existing GNN encoder. Extensive experiments on popular benchmark datasets show that incorporating prompt learning significantly improves (3% - 15%) the performance of state-of-the-art GNN models in crystal property prediction tasks. Furthermore, the learned soft prompts enable cross-property knowledge transfer, enhancing prediction performance for properties with limited training data. Code is available at https://github.com/shrimonmuke0202/Prompt.git' volume: 337 URL: https://proceedings.mlr.press/v337/mukherjee26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/mukherjee26a/mukherjee26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-mukherjee26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shrimon family: Mukherjee - given: Kishalay family: Das - given: Partha family: Basuchowdhuri - given: Pawan family: Goyal - given: Niloy family: Ganguly editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4661-4683 id: mukherjee26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4661 lastpage: 4683 published: 2026-08-06 00:00:00 +0000 - title: 'Online Bootstrap Inference for the Trend of Nonstationary Time Series' abstract: 'This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including exponential smoothing methods and moving averages. The bootstrap procedure is motivated by asymptotic arguments and provides well-calibrated uniform-in-time coverage, enabling scalable uncertainty quantification in streaming or large-scale time-series settings. This makes the method suitable for tasks such as adaptive anomaly detection, online monitoring, or streaming A/B testing. Simulation studies demonstrate good finite-sample performance of our method across a range of nonstationary scenarios. In summary, this offers a practical resampling framework that complements online trend estimation with reliable statistical inference.' volume: 337 URL: https://proceedings.mlr.press/v337/nagler26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nagler26a/nagler26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nagler26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Thomas family: Nagler - given: Tobias family: Brock - given: Nicolai family: Palm editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4684-4711 id: nagler26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4684 lastpage: 4711 published: 2026-08-06 00:00:00 +0000 - title: 'IDCR: Information-Directed Conformal Retrieval' abstract: 'Retrieval-augmented prediction systems select documents by semantic similarity, ignoring their effect on downstream predictive uncertainty. In high-stakes domains such as clinical diagnosis, this can yield overconfident or needlessly imprecise predictions. We propose Information-Directed Conformal Retrieval, a framework that selects documents to minimize the volume of conformal prediction sets while preserving distribution-free coverage. Modeling each document as a {Bayesian} precision update, we show that minimizing conformal volume is exactly equivalent to maximizing a log-determinant objective, and prove this objective monotone submodular, so greedy selection inherits the constant-factor $(1-1/e)$ guarantee. A Document Interaction Tensor characterizes corpus-level interaction structure, and a lightweight marginal-gain-separation gate routes uncertain retrieval steps to lookahead search. On MIMIC-IV clinical diagnosis (275 admissions from 100 patients, 9273 PubMed abstracts), greedy retrieval attains a mean greedy-to-optimal ratio of 0.9999, produces conformal ellipsoids 4.8 times smaller than random retrieval and 5.8 times smaller than cosine retrieval while retaining the distribution-free coverage guarantee, and two-step lookahead closes 77 percent of the remaining gap. Gains generalize to the SciQ and GoEmotions benchmarks, and on GoEmotions and LexGLUE the method yields tighter posterior uncertainty than learned and uncertainty-aware retrieval baselines. Complex multi-morbid patients benefit most, with twice the synergy-gap rate, precisely where prediction is hardest.' volume: 337 URL: https://proceedings.mlr.press/v337/nanivadekar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nanivadekar26a/nanivadekar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nanivadekar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Manas family: Nanivadekar - given: Jatin family: Khanijoan - given: Swayam family: Kothekar - given: Mohd Amaan family: Khan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4712-4732 id: nanivadekar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4712 lastpage: 4732 published: 2026-08-06 00:00:00 +0000 - title: 'Dynamics of Learning under User Choice: Overspecialization and Peer-Model Probing' abstract: 'In many economically relevant contexts where machine learning is deployed, multiple platforms obtain data from the same pool of users, each of whom selects the platform that best serves them. Prior work in this setting focuses exclusively on the “local” losses of learners on the distribution of data that they observe. We find that there exist instances where learners who use existing algorithms almost surely converge to models with arbitrarily poor global performance, even when models with low full-population loss exist. This happens through a feedback-induced mechanism, which we call the overspecialization trap: as learners optimize for users who already prefer them, they become less attractive to users outside this base, which further restricts the data they observe. Inspired by the recent use of knowledge distillation in modern ML, we propose an algorithm that allows learners to "probe" the predictions of peer models, enabling them to learn about users who do not select them. Our analysis characterizes when probing succeeds: this procedure converges almost surely to a stationary point with bounded full-population risk when probing sources are sufficiently informative, e.g., a known market leader or a majority of peers with good global performance. We verify our findings with semi-synthetic experiments on the MovieLens, Census, and Amazon Sentiment datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/narang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/narang26a/narang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-narang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Adhyyan family: Narang - given: Sarah family: Dean - given: Lillian J. family: Ratliff - given: Maryam family: Fazel editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4733-4772 id: narang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4733 lastpage: 4772 published: 2026-08-06 00:00:00 +0000 - title: 'What Capable Agents Must Know: Selection Theorems for Robust Decision-Making under Uncertainty' abstract: 'As artificial agents become increasingly capable, what internal structure is *necessary* for an agent to act competently under uncertainty? Classical results show that optimal control can be *implemented* using belief states or world models, but not that such representations are required. We prove quantitative "selection theorems" showing that strong task performance (low *average-case regret*) forces world models, belief-like memory and—under task mixtures—persistent regime-tracking variables resembling functional primitives of emotion, along with informational modularity under block-structured tasks. Our results cover stochastic policies, partial observability, and evaluation under task distributions, without assuming optimality, determinism, or access to an explicit model. Technically, we reduce predictive modeling to binary "betting" decisions and show that regret bounds limit probability mass on suboptimal bets, enforcing the predictive distinctions needed to separate high-margin outcomes. In fully observed settings, this yields approximate recovery of the interventional transition kernel; under partial observability, it implies necessity of predictive state and belief-like memory, addressing an open question in prior world-model recovery work.' volume: 337 URL: https://proceedings.mlr.press/v337/nayebi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nayebi26a/nayebi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nayebi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Aran family: Nayebi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4773-4795 id: nayebi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4773 lastpage: 4795 published: 2026-08-06 00:00:00 +0000 - title: 'Adaptive and Robust Watermark for Generative Tabular Data' abstract: 'In recent years, watermarking generative tabular data has become a prominent framework to protect against the misuse of synthetic data. However, while most prior work in watermarking methods for tabular data demonstrate a wide variety of desirable properties (e.g., high fidelity, detectability, robustness), the findings often emphasize empirical guarantees against common oblivious and adversarial attacks. In this paper, we study a flexible and robust watermarking algorithm for generative tabular data. Specifically, we demonstrate theoretical guarantees on the performance of the algorithm on metrics like fidelity, detectability, robustness, and hardness of decoding. The proof techniques introduced in this work may be of independent interest and may find applicability in other areas of machine learning. Finally, we validate our theoretical findings on synthetic and real-world tabular datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/ngo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ngo26a/ngo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ngo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Dung Daniel family: Ngo - given: Archan family: Ray - given: Akshay family: Seshadri - given: Daniel family: Scott - given: Saheed family: Obitayo - given: Niraj family: Kumar - given: Vamsi K. family: Potluru - given: Marco family: Pistoia - given: Manuela family: Veloso editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4796-4831 id: ngo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4796 lastpage: 4831 published: 2026-08-06 00:00:00 +0000 - title: 'REALITrees: Rashomon Ensemble Active Learning for Interpretable Trees' abstract: 'Active learning reduces labeling costs by querying samples to maximize information gain. A dominant framework, Query-by-Committee, typically relies on *perturbation-based diversity* by inducing model disagreement through random feature subsetting or data blinding. While this approximates one notion of epistemic uncertainty, it sacrifices direct characterization of the plausible hypothesis space. We propose the complementary approach: *{Rashomon} Ensembled Active Learning (REAL)* which constructs a committee by exhaustively enumerating the {Rashomon} Set of all near-optimal models. To address functional redundancy within this set, we adopt a Probably Approximately Correct-{Bayesian} framework using a {Gibbs} posterior to weigh committee members by their empirical risk. Leveraging recent algorithmic advances, we exactly enumerate this set for the class of sparse decision trees. Across synthetic and established active learning baselines, REAL outperforms randomized ensembles, particularly in moderately noisy environments where it leverages expanded model multiplicity to achieve faster convergence.' volume: 337 URL: https://proceedings.mlr.press/v337/nguyen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nguyen26a/nguyen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nguyen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Simon Dovan family: Nguyen - given: Hayden family: McTavish - given: Kentaro family: Hoffman - given: Tyler family: McCormick - given: Cynthia family: Rudin editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4832-4854 id: nguyen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4832 lastpage: 4854 published: 2026-08-06 00:00:00 +0000 - title: 'Tight rates of approximation of mixed Nash equilibria by entropy regularization in continuous games' abstract: 'We study how well the quantal response equilibrium ({QRE}) approximates the mixed {Nash} equilibrium ({MNE}) in two-player zero-sum games, as a function of the inverse temperature $\beta$. We introduce a reduction framework that decomposes the worst-case Nikaido–Isoda error of the {QRE} into a sum of two independent single-player {Gibbs} concentration problems, enabling tight matching bounds across a range of payoff classes. For finite games with $M \times N$ payoff matrices, we establish a tight rate of $\Theta(\beta^{-1}(\log M + \log N))$. For games with $\alpha$-Hölder-continuous payoffs on the torus, we prove a lower bound of $\Omega((d_x+d_y)/(\alpha\beta))$ and an upper bound of $O((d_x+d_y)\log(L\beta)/(\alpha\beta))$; whether the logarithmic gap is tight is left as an open problem. For smooth payoffs with sparse non-degenerate {MNE}, we prove that every individual game achieves a rate of $(d_x + d_y)/(2\beta) + O(1/\beta^2)$ via {Laplace} concentration, and that this rate is tight.' volume: 337 URL: https://proceedings.mlr.press/v337/nguyen26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nguyen26b/nguyen26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nguyen26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Khang family: Nguyen - given: Valentio family: Iverson - given: Sahan family: Wijetunga - given: William family: Chang - given: Guillaume family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4855-4872 id: nguyen26b issued: date-parts: - 2026 - 8 - 6 firstpage: 4855 lastpage: 4872 published: 2026-08-06 00:00:00 +0000 - title: 'When Does Model Multiplicity Affect Prediction Intervals? A Sharp Phase Transition' abstract: 'The {Rashomon} effect, the fact that many different models can achieve nearly identical predictive accuracy, has been extensively studied across various domains of machine learning. While modern conformal prediction provides valid intervals for a single model, it remains blind to the inherent arbitrariness of having to select from multiple candidates. This paper bridges this gap by investigating when model multiplicity, or the existence of many near-optimal models, materially widens prediction intervals. We prove a sharp phase transition for ridge regression under {Gaussian} design and introduce *{Rashomon} Prediction Intervals* (RPIs), which bound the range of predictions across the {Rashomon} set and establish a {Rashomon}-Conformal Bridge that provides distribution-free coverage guarantees. A critical tolerance $\varepsilon^\star = \Theta(\sigma^2/p)$ separates two distinct regimes: below it, {Rashomon}-conformal intervals match standard conformal width; above it, model multiplicity dominates, and this scaling is provably minimax optimal. Computationally, exact RPIs are polynomial for convex classes but NP-hard for tree ensembles, with a thin-cap volumetric barrier ruling out sampling-based approximation. Experiments on six UCI benchmarks confirm the phase transition, with all datasets falling in the sub-critical regime at standard tolerances, indicating that model multiplicity is invisible in prediction intervals for typical tabular regression.' volume: 337 URL: https://proceedings.mlr.press/v337/nguyen26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nguyen26c/nguyen26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nguyen26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hai family: Nguyen - given: Khanh family: Nguyen - given: Hung family: Mai - given: Luong family: Doan - given: Nhung family: Duong - given: Phong family: Ho - given: Tuan family: Do editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4873-4889 id: nguyen26c issued: date-parts: - 2026 - 8 - 6 firstpage: 4873 lastpage: 4889 published: 2026-08-06 00:00:00 +0000 - title: 'MUSS: Multilevel Subset Selection for Relevance and Diversity' abstract: 'The problem of relevant and diverse subset selection has a wide range of applications, including recommender systems and retrieval-augmented generation (RAG). For example, in recommender systems, one is interested in selecting relevant items, while providing a diversified recommendation. Constrained subset selection problem is NP-hard, and popular approaches such as Maximum Marginal Relevance (MMR ) are based on greedy selection. Many real-world applications involve large data, but the original MMR work did not consider distributed selection. This limitation was later addressed by a method called DGDS which allows for a distributed setting using random data partitioning. Here, we exploit structure in the data to further improve both scalability and performance on the target application. We propose MUSS, an efficient method that uses a multilevel approach to relevant and diverse selection. In a recommender system application, our method can not only improve the performance up to 4 percent points in precision, but is also 20 to 80 times faster. Our method is also capable of outperforming baselines on RAG-based question answering accuracy. We present a novel theoretical approach for analyzing this type of problems, and show that our method achieves a constant factor approximation of the optimal objective. Moreover, our analysis also results in a x2 tighter bound for DGDS compared to previously known bound. Our code is publicly available at https://github.com/amazon-science/muss.' volume: 337 URL: https://proceedings.mlr.press/v337/nguyen26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nguyen26d/nguyen26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nguyen26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Vu family: Nguyen - given: Andrey family: Kan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4890-4913 id: nguyen26d issued: date-parts: - 2026 - 8 - 6 firstpage: 4890 lastpage: 4913 published: 2026-08-06 00:00:00 +0000 - title: 'Mixture-Greedy for Online Generative Model Selection: Is UCB Necessary in Diversity-Aware Multi-Armed Bandits?' abstract: 'Efficient selection among multiple generative models is increasingly important in modern generative {AI}, where sampling from suboptimal models is costly. This problem can be viewed as a *multi-armed bandit (MAB)* task. Under diversity-aware evaluation scores, a non-degenerate mixture of generators can outperform any individual model, distinguishing this MAB setting from classical best-arm identification. Prior approaches incorporate an Upper Confidence Bound ({UCB}) exploration bonus into the mixture objective. However, across multiple datasets and evaluation metrics, we observe that the {UCB} term consistently slows convergence and reduces sample efficiency. In contrast, a simple *Mixture-Greedy* strategy without explicit {UCB}-type optimism converges faster and achieves even better performance, particularly for widely used metrics such as FID and Vendi where tight confidence bounds are difficult to construct. We provide theoretical insight explaining this behavior: under structural conditions, diversity-aware objectives induce *implicit exploration* by favoring interior mixtures, leading to sampling of all arms and sublinear regret guarantees for diversity-based objectives. These results suggest that in diversity-aware multi-armed bandits, e.g., for generative model selection, exploration can arise intrinsically from the objective’s geometry. The project code is available at https://github.com/bhrdbn/Mixture-Greedy.' volume: 337 URL: https://proceedings.mlr.press/v337/nia26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nia26a/nia26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nia26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bahar Dibaei family: Nia - given: Farzan family: Farnia editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4914-4948 id: nia26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4914 lastpage: 4948 published: 2026-08-06 00:00:00 +0000 - title: 'Scaling Up Bayesian DAG Sampling' abstract: '{Bayesian} inference of {Bayesian} network structures is often performed by sampling directed acyclic graphs along an appropriately constructed {Markov} chain. We present two techniques to improve sampling. First, we give an efficient implementation of basic moves, which add, delete, or reverse a single arc. Second, we expedite summing over parent sets, an expensive task required for more sophisticated moves: we devise a preprocessing method to prune possible parent sets so as to approximately preserve the sums. Our empirical study shows that our techniques can yield substantial efficiency gains compared to previous methods.' volume: 337 URL: https://proceedings.mlr.press/v337/nikzad26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nikzad26a/nikzad26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nikzad26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Daniele family: Nikzad - given: Alexander family: Zhilkin - given: Juha family: Harviainen - given: Jack family: Kuipers - given: Giusi family: Moffa - given: Mikko family: Koivisto editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4949-4971 id: nikzad26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4949 lastpage: 4971 published: 2026-08-06 00:00:00 +0000 - title: 'Conformal Risk Minimization with Variance Reduction' abstract: 'Conformal prediction **({CP})** is a distribution-free framework for achieving probabilistic guarantees on black-box models. **{CP}** is generally applied to a model post-training. Recent research efforts, on the other hand, have focused on optimizing {CP} efficiency **during training**. We formalize this concept as the problem of **conformal risk minimization** (CRM). In this direction, **conformal training** **(ConfTr**) by (Stutz et. al (2022)) is a CRM technique that seeks to minimize the expected prediction set size of a model by simulating **{CP}** in-between training updates. In this paper, we provide a novel analysis for the **ConfTr** gradient estimation method, revealing a strong source of sample inefficiency that introduces training instability and limits its practical use. To address this challenge, we propose **variance-reduced conformal training** **(VR-ConfTr)**, a CRM method that carefully incorporates a novel variance reduction technique in the gradient estimation of the **ConfTr** objective function. Through extensive experiments on various benchmark datasets, we demonstrate that **VR-ConfTr** consistently achieves faster convergence and smaller prediction sets compared to baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/noorani26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/noorani26a/noorani26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-noorani26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sima family: Noorani - given: Orlando family: Romero - given: Nicolo family: Dal Fabbro - given: Hamed family: Hassani - given: George J. family: Pappas editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 4972-5002 id: noorani26a issued: date-parts: - 2026 - 8 - 6 firstpage: 4972 lastpage: 5002 published: 2026-08-06 00:00:00 +0000 - title: 'What Type of Inference is Active Inference?' abstract: 'Active inference casts decision-making as inference, with the Expected Free Energy (EFE) providing an objective that unifies goal-seeking and information-gathering behavior. Recent work showed that EFE minimization can be reformulated as Variational Free Energy (VFE) minimization on a generative model augmented with epistemic priors, but left open how this formulation relates to other inference-based planning methods and whether it admits efficient message-passing implementations. Here we address both questions. First, we show that active inference is variational inference with specific entropy corrections to the VFE. Different planning-as-inference methods correspond to different corrections, each yielding a distinct objective; active inference is the variant whose corrections yield the Expected Free Energy. Second, we derive a message-passing scheme by introducing a channel reparameterization that re-localizes the entropy corrections into a standard Bethe free energy. Experiments on three grid-world environments with distinct uncertainty profiles show that the dynamics channel drives spatial information gathering when observations are decisive, the observation channel is critical when observations are merely suggestive, and only the full active inference objective performs robustly across all regimes.' volume: 337 URL: https://proceedings.mlr.press/v337/nuijten26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/nuijten26a/nuijten26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-nuijten26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Wouter W. L. family: Nuijten - given: Mykola family: Lukashchuk - given: Thijs prefix: van de family: Laar - given: Bert prefix: de family: Vries editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5003-5039 id: nuijten26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5003 lastpage: 5039 published: 2026-08-06 00:00:00 +0000 - title: 'Prior-Fitted Functional Flows: In-Context Generative Models for Pharmacokinetics' abstract: 'We introduce Prior-Fitted Functional Flows, a generative foundation model for pharmacokinetics that enables zero-shot population synthesis and individual forecasting without manual parameter tuning. We learn functional vector fields, explicitly conditioned on the sparse, irregular data of an entire study population. This enables the generation of coherent virtual cohorts as well as forecasting of partially observed patient trajectories with calibrated uncertainty. We construct a new open-access literature corpus to validate our priors, and demonstrate state-of-the-art predictive accuracy on extensive real-world datasets. Our code repository a, pretrained model, data and examples are available online.' volume: 337 URL: https://proceedings.mlr.press/v337/ojeda26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ojeda26a/ojeda26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ojeda26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: César family: Ojeda - given: Niklas family: Hartung - given: Purity Kamene family: Kavwele - given: Tim family: Jahn - given: Piyush family: Kumar - given: Marian family: Klose - given: Wilhelm family: Huisinga - given: Ramsés J family: Sánchez - given: Darius A family: Faroughy editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5040-5059 id: ojeda26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5040 lastpage: 5059 published: 2026-08-06 00:00:00 +0000 - title: 'MetaCaDI: A Meta-Learning Framework for Causal Discovery from Multiple Environments with Unknown Interventions' abstract: 'Uncovering the causal mechanisms of complex real-world systems remains a significant challenge, as these systems often entail high data collection costs and involve unknown interventions. We introduce MetaCaDI, the first framework to cast the identification of unknown interventions as a meta-learning problem, explicitly leveraging a jointly learned causal graph. MetaCaDI is a {Bayesian} framework that learns a shared causal structure across multiple environments and is optimized to rapidly adapt to new, few-shot intervention target identification tasks. A key innovation is our model’s analytical adaptation, which uses a closed-form solution to bypass expensive and potentially unstable gradient-based bilevel optimization. Extensive experiments on synthetic and complex gene expression data demonstrate that MetaCaDI significantly outperforms state-of-the-art methods. It excels at identifying intervention targets from as few as 3 samples—where existing methods collapse to random chance—while robustly recovering the shared causal graph, proving its effectiveness in data-scarce scenarios.' volume: 337 URL: https://proceedings.mlr.press/v337/ong26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ong26a/ong26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ong26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hans Jarett family: Ong - given: Yoichi family: Chikahara - given: Tomoharu family: Iwata editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5060-5080 id: ong26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5060 lastpage: 5080 published: 2026-08-06 00:00:00 +0000 - title: 'Falsifying Causal Graphs With Outlier Events' abstract: 'True causal relationships are rarely known, and inferring causal graphs from data is hard. A fundamental challenge is how to assess whether a given causal graph is good in the absence of a ground truth. We propose falsifying candidate causal graphs based on whether they can explain the propagation of an outlier event. Our approach leverages a key principle: weak outliers rarely cause strong ones. While this principle has previously been used in root cause analysis to identify root causes without prior knowledge of the graph, we turn it on its head and use it to falsify candidate causal graphs whose implied outlier propagation is inconsistent with the data. To this end, we present the first statistical tests for the hypothesis that a candidate graph is the true causal graph, and show they have false positive control, power guarantees against incorrect causal graphs, and can operate with a single outlier sample.' volume: 337 URL: https://proceedings.mlr.press/v337/orchard26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/orchard26a/orchard26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-orchard26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: William Roy family: Orchard - given: Philipp Michael family: Faller - given: Dominik family: Janzing editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5081-5110 id: orchard26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5081 lastpage: 5110 published: 2026-08-06 00:00:00 +0000 - title: 'Partially Observed Structural Causal Models' abstract: 'Here we introduce Partially Observed Structural Causal Models (POSCMs) as an extension of structural causal models (SCMs) to settings where upstream contexts co-determine both the interaction structure and downstream mechanisms on observed variables. POSCMs thus provide a self-contained causal modeling framework for endogenous graphs, allowing for an intervention hierarchy spanning node- and edge-level contexts and endogenous variable interventions. To define edge interventions, we separate node mechanisms into edge-local transmission channels that can be modified without changing the source node or the rest of the target mechanism. We provide an identifiability theory that clarifies which intervention families would suffice to disentangle structure formation from mechanisms. We then empirically validate these theoretical results in two external simulators: a biophysically detailed virtual human retina and a gene-regulatory analogue. The experiments reproduce non-identifiability under latent context, expose structure-mechanism confounding under latent edges, and recover pathway-level input-output relationships under targeted interventions, consistent with our positive {Markov} kernel identifiability results. Together, POSCMs provide an intervention-oriented framework for causal systems in which contexts, graph structure, mechanisms, and measurements are jointly generated and only partially observed.' volume: 337 URL: https://proceedings.mlr.press/v337/orujlu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/orujlu26a/orujlu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-orujlu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Turan family: Orujlu - given: Jordan Kyle family: Matelsky - given: Martin V. family: Butz - given: Charley M family: Wu - given: Konrad family: Kording editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5111-5137 id: orujlu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5111 lastpage: 5137 published: 2026-08-06 00:00:00 +0000 - title: 'Coarsening Bias from Variable Discretization in Causal Functionals' abstract: 'Causal identification functionals often require integration over conditional densities of continuous variables, such as those arising in nonparametric identification theory of total and mediated causal effects in DAGs with hidden variables. Estimating these densities and evaluating the resulting integrals can be statistically and computationally demanding. A common workaround is to discretize the continuous variable and replace integrals with finite sums. Although convenient, discretization alters the population-level functional and can induce non-negligible approximation bias, even when identification is correct. Under smoothness conditions, we show that the resulting coarsening error is first order in the bin width and arises at the level of the target functional, distinct from statistical estimation error. We propose a simple debiased coarsened functional that evaluates the outcome regression at within-bin conditional means, eliminating the leading coarsening error term and yielding a second-order approximation error. We derive plug-in and one-step estimators for this debiased coarsened functional. Simulations demonstrate substantial bias reduction and near-nominal confidence interval coverage, even under coarse binning. Our results provide a simple framework for controlling the impact of variable discretization on both parameter approximation and statistical estimation.' volume: 337 URL: https://proceedings.mlr.press/v337/ou26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ou26a/ou26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ou26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xiaxian family: Ou - given: Razieh family: Nabi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5138-5167 id: ou26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5138 lastpage: 5167 published: 2026-08-06 00:00:00 +0000 - title: 'Sample-Efficient Learning of Probabilistic Causes for Reachability in Markov Decision Processes with Probabilistic Guarantees' abstract: 'Probabilistic model checking for {Markov} decision processes ({MDPs}) provides quantitative guarantees, but often offers limited insight into why undesired outcomes occur. Probability-raising (PR) causality addresses this by identifying states whose visitation increases the probability of reaching designated states. Existing PR-cause identification methods, however, use {MDP} modifications ill-suited for learning: the gap between conditional and unconditional reachability probabilities can be hard to detect from samples, and construction requires reachability probabilities of the original {MDP}, which are unavailable when transition probabilities are unknown. We study unknown {MDPs} and propose a learning approach with probabilistic guarantees for PR-cause identification. Our key ingredient is a restart-based {MDP} modification that reduces PR-cause checking to two conditional reachability queries without using reachability values of the original {MDP}. We prove correctness, establish sample-complexity bounds, and develop an anytime learning-and-checking algorithm based on two-sided value iteration that progressively classifies states as causal, non-causal, or undecided. Experiments on two benchmarks demonstrate reliable and fast identification of PR causes.' volume: 337 URL: https://proceedings.mlr.press/v337/oura26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/oura26a/oura26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-oura26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ryohei family: Oura - given: Georgios family: Fainekos - given: Hideki family: Okamoto - given: Bardh family: Hoxha editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5168-5196 id: oura26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5168 lastpage: 5196 published: 2026-08-06 00:00:00 +0000 - title: 'Explore, Refine, then Commit: Nearly Optimal Multi-Group Mean Estimation with Active Learning' abstract: 'We present nearly optimal algorithms for simultaneously estimating the means of multiple distributions given a fixed total sample budget while ensuring uniform confidence intervals for the distributions. Our algorithms are based on the well-known _explore-then-commit_ policy from the bandit literature along with an additional refinement phase between the exploration phase and the commit phase. Our algorithms achieve regret $\tilde{O}( (\log \sigma_{\min}^{-1})^{0.5} T^{-1.5})$ when the rewards are subgaussian and $\tilde{O}(\sigma_{\min}^{-1}T^{-1.5})$ regret when the rewards have bounded fourth moment, where $T$ is the horizon and $\sigma_{\min}^2$ is the minimum among the variances of the distributions of the $G$ arms. We also provide lower bounds on the regret that nearly match the upper bounds for a constant $G$ in both these cases. IImportantly, we show that the dependence on $\sigma_{\min}$ in both cases is necessary, resolving a long-standing open problem of [Carpentier et al]. We also study the setting where the distributions are hypercontractive. This distribution class includes the family of {Gaussian} distributions but also includes several families of heavy-tailed distributions. We propose an algorithm for hypercontractive reward distributions that achieves a $\tilde{O}(T^{-1.5})$ regret, independent of $\sigma_{\min}$, and show a nearly matching lower bound for Gaussians.' volume: 337 URL: https://proceedings.mlr.press/v337/pandey26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/pandey26a/pandey26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-pandey26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shourya family: Pandey - given: Syamantak family: Kumar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5197-5243 id: pandey26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5197 lastpage: 5243 published: 2026-08-06 00:00:00 +0000 - title: 'The Convergence Behavior of Adam under Heavy-Tailed Noise' abstract: 'We establish the first convergence guarantees for the plain vector-form \emph{{Adam}} optimizer under heavy-tailed stochastic noise. While several {Adam} variants are known to achieve optimal iteration complexity in bounded-variance nonconvex optimization, little is understood about their behavior when stochastic gradients admit only a bounded $p$-th central moment for some $p \in (1,2]$, a setting increasingly observed in modern deep learning. To address this gap, we generalize the recent online-to-nonconvex conversion framework to accommodate heavy-tailed martingale-difference noise. Building on this generalized framework, we develop a discounted regret analysis for {Adam}, without restrictive parameter coupling. Our results show that {Adam} converges to $(\rho,\epsilon)$-stationary points under heavy-tailed noise. However, it exhibits a suboptimal iteration complexity and $p$-dependent convergence, a suboptimality that persists even in the bounded-variance case ($p=2$). When the domain radius is known and used to control the online-learner output, a standard setup in related literature, the convergence rate improves to match the optimal complexity. These findings provide new theoretical insight into the robustness and limitations of {Adam} in heavy-tailed regimes.' volume: 337 URL: https://proceedings.mlr.press/v337/pang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/pang26a/pang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-pang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yijiang family: Pang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5244-5265 id: pang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5244 lastpage: 5265 published: 2026-08-06 00:00:00 +0000 - title: 'On Transportability for Structural Causal Bandits' abstract: 'The structural causal bandit (SCB) framework offers a graphical approach to identifying suboptimal actions by leveraging prior knowledge of the underlying causal structure. While theoretically appealing, there has been limited guidance on how to systematically transfer information across heterogeneous datasets from multiple environments. In this paper, we study the structural causal bandit under transportability, where prior knowledge from source environments is integrated to accelerate learning in a target deployment environment. We show that exploiting causal invariances across environments improves sample efficiency in identifying the optimal action.' volume: 337 URL: https://proceedings.mlr.press/v337/park26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/park26a/park26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-park26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Min Woo family: Park - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5266-5288 id: park26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5266 lastpage: 5288 published: 2026-08-06 00:00:00 +0000 - title: 'Breaking Bad: Component-Wise Parent Deletion for Score-Based Causal Discovery' abstract: 'Directed acyclic graphs (DAGs) are widely used to represent complex causal relationships in real-world systems. The goal of causal discovery is to learn the underlying {DAG} from data generated by these systems. While *Greedy Equivalence Search* (GES) is a well-established score-based algorithm for causal discovery, the GES family often suffers from scalability and sample complexity issues due to its large search space and susceptibility to local optima. In this paper, we introduce *parent deletion*, a novel, simple, yet powerful operator for score-based causal discovery. This operator is theoretically sound and effectively alleviates these limitations. Moreover, its simplicity enables seamless compatibility with existing score-based methods, and extensive experiments demonstrate consistent improvements across a wide range of settings. The source code used in this study is available at https://github.com/LGAI-Research/breaking-bad.' volume: 337 URL: https://proceedings.mlr.press/v337/park26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/park26b/park26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-park26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Min Woo family: Park - given: Taehui family: Yun - given: YoungIn family: Jang - given: Yoonseok family: Yeom - given: Jonghwan family: Kim - given: Jiyeon family: Kang - given: Songseong family: Kim - given: Hyemin family: Jung - given: Sangmin family: Lee - given: Jongseong family: Jang - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5289-5331 id: park26b issued: date-parts: - 2026 - 8 - 6 firstpage: 5289 lastpage: 5331 published: 2026-08-06 00:00:00 +0000 - title: 'Higher-Order Hit-&-Run Samplers for Linearly Constrained Densities' abstract: '{Markov} chain Monte Carlo ({MCMC}) sampling of densities restricted to linearly constrained domains is an important task arising in {Bayesian} treatment of inverse problems in the natural sciences. While efficient algorithms for uniform polytope sampling exist, much less work has dealt with more complex constrained densities. In particular, gradient information as used in unconstrained {MCMC} is not necessarily helpful in the constrained case, where the gradient may push the proposal’s density out of the polytope. In this work, we propose a novel constrained sampling algorithm, which combines strengths of higher-order information, like the target’s log-density’s gradients and curvature, with the Hit-&-Run proposal, a simple mechanism which guarantees the generation of feasible proposals, fulfilling the linear constraints. Our extensive experiments demonstrate improved sampling efficiency on complex constrained densities over various constrained and unconstrained samplers.' volume: 337 URL: https://proceedings.mlr.press/v337/paul26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/paul26a/paul26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-paul26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Richard D. family: Paul - given: Anton family: Stratmann - given: Johann F. family: Jadebeck - given: Martin family: Beyß - given: Hanno family: Scharr - given: David family: Rügamer - given: Katharina family: Nöh editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5332-5355 id: paul26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5332 lastpage: 5355 published: 2026-08-06 00:00:00 +0000 - title: 'Information Theoretic Bayesian Optimization over the Probability Simplex' abstract: '{Bayesian} optimization is a data-efficient technique that has been shown to be extremely powerful to optimize expensive, black-box, and possibly noisy objective functions. Many applications involve optimizing probabilities and mixtures which naturally belong to the probability simplex, a constrained non-{Euclidean} domain defined by non-negative entries summing to one. This paper introduces $\alpha$-GaBO, a novel family of {Bayesian} optimization algorithms over the probability simplex. Our approach is grounded in information geometry, a branch of Riemannian geometry which endows the simplex with a Riemannian metric and a class of connections. Based on information geometry theory, we construct Matérn kernels that reflect the geometry of the probability simplex, as well as a one-parameter family of geometric optimizers for the acquisition function. We validate our method on benchmark functions and on a variety of real-world applications including mixtures of components, mixtures of classifiers, and a robotic control task, showing its increased performance compared to constrained {Euclidean} approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/pavesi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/pavesi26a/pavesi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-pavesi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Federico family: Pavesi - given: Antonio family: Candelieri - given: Noémie family: Jaquier editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5356-5373 id: pavesi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5356 lastpage: 5373 published: 2026-08-06 00:00:00 +0000 - title: 'How Predicted Links Influence Network Evolution: Disentangling Choice and Algorithmic Feedback in Dynamic Graphs' abstract: 'Link prediction models are increasingly used to recommend interactions in evolving networks, yet their impact on network structure is typically assessed from static snapshots. In particular, observed homophily conflates intrinsic interaction tendencies with amplification effects induced by network dynamics and algorithmic feedback. We propose a temporal framework based on multivariate Hawkes processes that disentangles these two sources and introduce an instantaneous bias measure derived from interaction intensities, capturing current reinforcement dynamics beyond cumulative metrics. We provide a theoretical characterization of the stability and convergence of the induced dynamics, and experiments show that the proposed measure reliably reflects algorithmic feedback effects across different link prediction strategies.' volume: 337 URL: https://proceedings.mlr.press/v337/perez26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/perez26a/perez26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-perez26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mathilde family: Perez - given: Raphaël family: Romero - given: Jefrey family: Lijffijt - given: Charlotte family: Laclau editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5374-5392 id: perez26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5374 lastpage: 5392 published: 2026-08-06 00:00:00 +0000 - title: 'Bayesian Experimental Design via Score Matching' abstract: 'Policy-based approaches to {Bayesian} experimental design (BED) allow the learning of deep policy networks that adaptively make intelligent design decisions based on previously collected data. However, the training of such policies is often held back by a fundamental challenge: the double intractability of the expected information gain (EIG). This necessitates expensive or complex approximations that restrict the effort one can invest in optimising the policy itself. To address this, we show that the double intractability of the EIG can be isolated from the policy learning by first solving a score matching problem that is independent of the policy used, then using the learned score approximation to train the policy in a singly intractable manner. This turns the key multiplicative cost into an additive one and reduces the computational burden on the policy training itself, making it far cheaper to train the policy multiple times when needed, e.g. for architecture search, hyperparameter tuning, or avoiding local optima. In our experiments we train multiple competitive policies without inducing a multiplicative cost in likelihood evaluations, which can increase performance by allowing us to select the best policy even without performing hyperparameter or architecture searches.' volume: 337 URL: https://proceedings.mlr.press/v337/phillips26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/phillips26a/phillips26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-phillips26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Angus family: Phillips - given: Gavin family: Kerrigan - given: Tom family: Rainforth editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5393-5426 id: phillips26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5393 lastpage: 5426 published: 2026-08-06 00:00:00 +0000 - title: 'Semantic Self-Distillation for Language Model Uncertainty' abstract: 'Large language models present challenges for principled uncertainty quantification, in part due to their complexity and the diversity of their outputs. Semantic dispersion, or the variance in the meaning of sampled answers, has been proposed as a useful proxy for model uncertainty, but the associated computational cost prohibits its use in latency-critical applications. We show that sampled semantic distributions can be distilled into lightweight student models which estimate a prompt-conditioned density before the language model generates an answer token. The student model predicts a semantic distribution over possible answers; the entropy of this distribution provides a prompt-level uncertainty signal, and the probability density allows answer-level reliability evaluation. Across experiments on TriviaQA and MMLU, we find our student models perform competitively relative to the teacher’s sampled semantic dispersion on a hallucination prediction task, whilst offering additional uncertainty primitives for out-of-domain detection and multiple-choice answer selection. We term this technique Semantic Self-Distillation (SSD), which can serve as a general framework for distilling predictive uncertainty in complex output spaces beyond language.' volume: 337 URL: https://proceedings.mlr.press/v337/phillips26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/phillips26b/phillips26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-phillips26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Edward family: Phillips - given: Sean family: Wu - given: Fredrik K. family: Gustafsson - given: Boyan family: Gao - given: David A. family: Clifton editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5427-5447 id: phillips26b issued: date-parts: - 2026 - 8 - 6 firstpage: 5427 lastpage: 5447 published: 2026-08-06 00:00:00 +0000 - title: 'A Characterization of the Orthocomplement of the Tangent Space of Semiparametric Markov Models' abstract: 'Graphical models are ubiquitous in social and empirical science as they are intuitive and easy to use. These models belong to the broader class of {Markov} models, defined using solely conditional independence (CI) restrictions. In order to estimate a finite-dimensional target parameter in such models efficiently, semi-parametric theory provides a principled framework for constructing regular and asymptotically linear estimators via influence functions (IFs). These estimators are asymptotically normal and root-$n$ consistent. Characterizing the class of all influence functions for a target parameter is crucial for statistically efficient inference in these models. For models that are {Markov} relative to directed acyclic graphs (DAGs), the orthogonal complement of the tangent space is known, implying that for any target the class of all influence functions can be derived once an influence function is obtained. On the other hand, for {Markov} models not equivalent to a {DAG} model—such as ordinary {Markov} models associated with undirected graphs, chain graphs, or acyclic directed mixed graphs—the orthogonal complement has not been characterized, impeding semi-parametric inference in these models. We derive closed form expressions for the orthogonal complement of the tangent space for general {Markov} models and illustrate our results by characterizing the class of influence functions for the conditional mean parameter in several graphical models.' volume: 337 URL: https://proceedings.mlr.press/v337/phung26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/phung26a/phung26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-phung26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Trung Q. family: Phung - given: Ilya family: Shpitser editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5448-5470 id: phung26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5448 lastpage: 5470 published: 2026-08-06 00:00:00 +0000 - title: 'UnGuide: Learning to Forget with LoRA-Guided Diffusion Models' abstract: 'Large-scale text-to-image diffusion models pose safety and compliance risks due to their ability to generate harmful or undesirable content. Machine unlearning seeks to remove specific concepts from pretrained models while preserving overall generative quality. Low-Rank Adaptation ({LoRA}) enables parameter-efficient targeted forgetting, but naive {LoRA}-based unlearning often induces distributional shift, degrading fidelity and destabilizing sampling. In this paper, we propose UnGuide, a {LoRA}-based unlearning framework with stability-aware adaptive guidance. Our method dynamically modulates classifier-free guidance ({CFG}) based on early denoising trajectory variance. By estimating discrepancies between base and {LoRA}-adapted noise predictions during initial diffusion steps, UnGuide interpolates per prompt between the frozen and adapted models. High-variance trajectories receive stronger adapted-model guidance to enforce forgetting, while low-variance trajectories rely on the base model to preserve fidelity. This mechanism enables controlled concept suppression without prompt embedding modification or external segmentation. Experiments on object erasure and explicit content removal demonstrate improved forgetting efficacy and superior fidelity retention compared to existing {LoRA}-based approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/polowczyk26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/polowczyk26a/polowczyk26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-polowczyk26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Alicja family: Polowczyk - given: Agnieszka family: Polowczyk - given: Dawid family: Malarz - given: Artur family: Kasymov - given: Jacek family: Tabor - given: Marcin family: Mazur - given: Przemysław family: Spurek editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5471-5503 id: polowczyk26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5471 lastpage: 5503 published: 2026-08-06 00:00:00 +0000 - title: 'Distributional Deep Gaussian Processes' abstract: 'Deep {Gaussian} processes (DGPs) offer a principled {Bayesian} framework with hierarchical uncertainty propagation, but their reliable propagation of uncertainty and out-of-distribution ({OOD}) detection performance remains underexplored and often unreliable in safety-critical settings. In this work, we propose a novel kernel operating in both {Euclidean} and {Wasserstein}-2 space to better account for the geometry of representation learning spaces, thus circumventing a common pathology called feature collapse, whereby inliers and outliers get mapped to similar spaces. Empirically, our approach consistently improves {OOD} detection in convolutional image tasks and shows improved performance on tabular datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/popescu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/popescu26a/popescu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-popescu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sebastian family: Popescu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5504-5540 id: popescu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5504 lastpage: 5540 published: 2026-08-06 00:00:00 +0000 - title: 'Transformer Based Bayesian Network Structure Learning from an Information Theory Perspective' abstract: 'The pivotal challenge of handling uncertainty in artificial intelligence has prompted a growing focus on learning {Bayesian} network ({BN}) structures from data in recent years. Nevertheless, most of the existing methods such as hill-climbing, variational auto-encoder and graph neural network-based algorithms continue to encounter the issues like local optimum and exponential computational complexity, etc. In response to these challenges, we propose a Transformer-based approach for learning the {BN} structure (T-{BNSL}) from an information theory perspective. Specifically, we first establish the graph skeleton of a {BN} by employing conditional independence tests grounded in mutual information. Subsequently, we propose a hill-climbing method with decomposable BIC scoring function to generate potential directed acyclic graphs (DAGs) and evaluate the BIC scores of a subset of these DAGs. Lastly, we use the Transformer framework with a refined attention module to predict the BIC scores of the remaining DAGs, enabling the efficient identification of the {DAG} with the highest score. Experimental findings demonstrate that our approach significantly surpasses state-of-the-art competitors in terms of accuracy and efficiency by several orders of magnitude when learning the {BN} structure.' volume: 337 URL: https://proceedings.mlr.press/v337/qi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/qi26a/qi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-qi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhiwei family: Qi - given: Kun family: Yue - given: Zhu family: Yang - given: Jiahui family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5541-5555 id: qi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5541 lastpage: 5555 published: 2026-08-06 00:00:00 +0000 - title: 'Reading As Humans: Unified Negation Detection via Cascade Linear Attention Network with Model-Agnostic Meta-Learning' abstract: 'Negation Detection (ND) aims to extract negative statements with non-factual semantics, including negative scopes, xscopes, focuses, where (x)scopes are continuous spans governed by negative cues, and focuses are the most principal negated texts in scopes. Previous studies are confined to task-specific models, and failed to develop a unified solution for (x)scopes and focuses based on the correlations of their definitions, nor implemented the mutual promotion for each task. Moreover, existing work did not design fine-grained encoders, resulting in reliance on external features, such as syntactic parse trees. To address these issues, we construct a unified negation detection paradigm with Model-Agnostic Meta-Learning (MAML) to facilitate those ND sub-tasks. Besides, inspired by reading mechanism of humans, we synthesize Cascade Linear Attention Network (CLAN) by heterogeneous linear attentions with cascade coefficients as fine-grained encoder. Experimental results on several corpora demonstrate that CLAN can outperform the state-of-the-arts.' volume: 337 URL: https://proceedings.mlr.press/v337/qian26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/qian26a/qian26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-qian26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhong family: Qian - given: Peifeng family: Li - given: Qiaoming family: Zhu - given: Guodong family: Zhou editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5556-5572 id: qian26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5556 lastpage: 5572 published: 2026-08-06 00:00:00 +0000 - title: 'Multi-Agent RL with Invisible Collaborators: Marginal Advantage Estimation for Indirect Cooperation' abstract: 'Cooperative Multi-Agent Reinforcement Learning ({MARL}) has primarily focused on direct cooperation among agents. However, many real-world systems exhibit structurally asymmetric cooperation, where agents are physically constrained and cannot directly coordinate with those on whom they depend. In such settings, accurately estimating individual contributions under high uncertainty is challenging. We propose Marginal Advantage Estimation (MAE), a representation-level contribution estimation method for cooperative {MARL} under this structural isolation. MAE employs a synchronised feature-masking mechanism to evaluate marginal contributions without action-level counterfactual perturbations, thereby reducing variance and providing more informative learning signals. We provide a theoretical analysis of its bias–variance properties and demonstrate consistent performance improvements across 18 tasks in Partitioned MPE and Basilisk benchmarks over strong cooperative {MARL} baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/qiao26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/qiao26a/qiao26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-qiao26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jianglin family: Qiao - given: Zehong family: Cao - given: Siyi family: Hu - given: Mingjun family: Fan - given: Mahardhika family: Pratama - given: Ryszard family: Kowalczyk editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5573-5600 id: qiao26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5573 lastpage: 5600 published: 2026-08-06 00:00:00 +0000 - title: 'Beyond Mean-Field: Tree-Copula Variational Autoencoders for Structured Latent Dependencies' abstract: 'Variational Autoencoders (VAEs) typically assume a factorized {Gaussian} posterior and isotropic normal prior, implicitly imposing mean-field independence in the latent space. Rewriting the {ELBO} in copula form, we isolate a dependence-mismatch term that contributes to approximation and amortization gaps. We propose a Tree-Copula VAE that replaces the mean-field posterior with a tree-structured copula while retaining flexible learned marginals. The tree is inferred per datapoint via a Chow–Liu maximum-weight spanning tree, exploiting the monotonic relationship between mutual information and copula parameters. We further study an Average-of-Trees (AoT) copula prior for prior–posterior alignment and a rank-1 {Gaussian}-copula likelihood for low-rank observation correlations. Experiments on correlated dSprites and Fashion-{MNIST} show tighter importance-weighted bounds than mean-field VAEs when latent dependence is present, and highlight the role of prior alignment and likelihood modeling beyond mean-field inference.' volume: 337 URL: https://proceedings.mlr.press/v337/rachamim26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/rachamim26a/rachamim26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-rachamim26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yarden family: Rachamim - given: Shai family: Fine editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5601-5622 id: rachamim26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5601 lastpage: 5622 published: 2026-08-06 00:00:00 +0000 - title: 'Metacognitive Arbitration as Uncertainty Compression in Multi-Agent Language Models' abstract: 'Multi-agent reasoning and metacognitive strategies are widely used to improve large language model ({LLM}) performance, yet the functional role of metacognition remains unclear. Prior methods often treat metacognition as a mechanism for generating better or more diverse reasoning. In this work, we argue that metacognition primarily functions as an information routing and compression mechanism rather than a generator of new reasoning content. We introduce MC-MAS, an inference-time framework that separates problem solving from metacognitive arbitration, where independent solvers propose candidate answers and an arbiter critiques and consolidates their outputs. Using routing-centric metrics: semantic novelty, entropy reduction, and overconfident errors across four reasoning benchmarks and multiple model settings, we show that MC-MAS introduces limited novelty but consistently reduces uncertainty and overconfidence, with accuracy gains that are modest and dataset-dependent. These results indicate that reliable improvements arise from structured arbitration rather than reflection or increased sampling alone.' volume: 337 URL: https://proceedings.mlr.press/v337/rahman26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/rahman26a/rahman26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-rahman26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mafizur family: Rahman - given: Lijun family: Qian editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5623-5642 id: rahman26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5623 lastpage: 5642 published: 2026-08-06 00:00:00 +0000 - title: 'Variance Estimation and Selecting Good Estimands for Causal Effect Queries' abstract: 'This paper investigates the statistical efficiency of algebraic expressions ("estimands") used to answer causal queries. We first examine structural rules, developing a partial dominance relationship for front-door estimands that extends recent results on back-door estimands. In many models, however, structural rules alone may be insufficient to select an estimand. For such cases, we propose empirical techniques for estimating and comparing the variance of different estimands using both the graph and observational data: 1) a bootstrap-based method, and 2) a computationally simpler yet practically effective method for discrete models which estimates the {Fisher} information matrices. We illustrate both methods’ effectiveness on a variety of causal diagrams and estimand forms.' volume: 337 URL: https://proceedings.mlr.press/v337/raichev26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/raichev26a/raichev26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-raichev26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Anna K family: Raichev - given: Rina family: Dechter - given: Jin family: Tian - given: Alexander family: Ihler editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5643-5660 id: raichev26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5643 lastpage: 5660 published: 2026-08-06 00:00:00 +0000 - title: 'Structure Learning for Unfaithful Distributions: The Minimal Dependence Faithfulness' abstract: 'Causal discovery algorithms such as {PC} often rely on faithfulness; yet {XOR}-type relations expose violations that {PC} and its weakened-faithfulness variants can miss. In such cases, a target variable $X$ may be independent of each variable $Y_i$ individually, while becoming dependent on $Y_i$ once the remaining variables are conditioned on. We call a minimal set with this property a minimal dependence (MD) set: no proper subset has the same dependence pattern. MD sets of size at least two violate faithfulness. We introduce minimal-dependence faithfulness and a corresponding orientation condition, characterize the resulting {DAG} structure by showing that dependent members of an MD set connect to $X$ directly or through colliders, and define the associated MD-equivalence representation. We then present MD-{PC}, a {PC}-style algorithm that detects such faithfulness violations and, under the proposed assumptions, returns the corresponding candidate class of DAGs.' volume: 337 URL: https://proceedings.mlr.press/v337/ramazi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/ramazi26a/ramazi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-ramazi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Pouria family: Ramazi - given: Hamid family: Kalantari editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5661-5676 id: ramazi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5661 lastpage: 5676 published: 2026-08-06 00:00:00 +0000 - title: 'Beyond Mixtures and Products for Ensemble Aggregation: A Likelihood Perspective on Generalized Means' abstract: 'Density aggregation is a central problem in machine learning, for instance when combining predictions from a Deep Ensemble. The choice of aggregation remains an open question with two commonly proposed approaches being linear pooling (probability averaging) and geometric pooling (logit averaging). In this work, we address this question by studying the normalized generalized mean of order $r \in \mathbb{R} \cup \{-\infty,+\infty\}$ through the lens of log-likelihood, the standard evaluation criterion in machine learning. This provides a unifying aggregation formalism and shows different optimal configurations for different situations. We show that the regime $r \in [0,1]$ is the only range ensuring systematic improvements relative to individual distributions, thereby providing a principled justification for the reliability and widespread practical use of linear ($r=1$) and geometric ($r=0$) pooling. In contrast, we show that aggregation rules with $r \notin [0,1]$ may fail to provide consistent gains with explicit counterexamples. Finally, we corroborate our theoretical findings with empirical evaluations using Deep Ensembles on image and text classification benchmarks.' volume: 337 URL: https://proceedings.mlr.press/v337/razafindralambo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/razafindralambo26a/razafindralambo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-razafindralambo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Raphaël family: Razafindralambo - given: Rémy family: Sun - given: Damien family: Garreau - given: Frederic family: Precioso - given: Pierre-Alexandre family: Mattei editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5677-5699 id: razafindralambo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5677 lastpage: 5699 published: 2026-08-06 00:00:00 +0000 - title: 'Expert Advice with Costly Observations' abstract: 'Querying expert predictions or human feedback incurs explicit, often heterogeneous costs—a challenge central to crowdsourcing and {LLM} training. We study online learning with expert advice under observation costs, where the learner must adaptively select which experts to query ($p_i$ is expert-dependent) to minimize cumulative cost (losses plus query costs). While classical bandits and recent paid observation models have advanced the field, they fail to capture the rich cost-adaptive selection landscape and do not provide tight, problem-dependent performance guarantees for heterogeneous costs. This paper provides the first comprehensive characterization. For adversarial losses, we prove tight minimax regret $\Theta(\underset{m\in\{1,…,K\}}{\min} \{\sqrt{\frac{K}{m}\,T\log K} + (m-1)\bar pT\}),$ interpolating between bandit and full-information regimes and revealing the optimal observation budget, where $\bar p$ is a tight upper bound of $p_i$s. For stochastic losses, our novel $m$-ELIM algorithm achieves instance-dependent regret of $O\left(\frac{\log T}{m}\sum_{i \neq i^*} \frac{1}{\Delta_i} + (m-1)\bar{p}T\right)$, $\Delta_i$ being the suboptimality gap of the $i$-th arm, showing how gap structure and costs interact. Matching lower bounds (adversarial and stochastic) establishes minimax optimality. These results provide the first rigorous framework for optimally allocating annotation budgets across heterogeneous workers in crowdsourcing systems, directly informing cost-effective strategies for collecting human feedback in adaptive learning applications.' volume: 337 URL: https://proceedings.mlr.press/v337/reyzin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/reyzin26a/reyzin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-reyzin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Lev family: Reyzin - given: Aadirupa family: Saha - given: Shuo family: Wu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5700-5715 id: reyzin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5700 lastpage: 5715 published: 2026-08-06 00:00:00 +0000 - title: 'Imprecise Probabilities for Privacy–Accuracy Trade-offs in Bayesian Networks' abstract: '{Bayesian} networks are well-known probabilistic graphical models that enable explainable reasoning under uncertainty. In many domains, data are scarce and fragmented across institutions, motivating collaboration and the sharing of learned models rather than individual-level records to increase the available evidence and reduce bias. Releasing a model, however, can still reveal sensitive information: adversaries may mount membership inference attacks to determine whether a specific individual contributed to the training. A common mitigation strategy is to inject noise into the learned model before its release. This perturbation may compromise the quality and interpretability of subsequent inferences. We investigate how a {Bayesian} network can be effectively masked rather than perturbed to protect it against attacks by leveraging credal networks, the imprecise version of {Bayesian} networks, allowing us to employ sets of parameters instead of exact point estimates. We formalize and compare various masking and attack strategies and investigate how privacy leakage depends on these strategies. Finally, we analyze how privacy and utility can be traded off in credal naive {Bayes} models, comparing them with the common noise-injection baseline. Results indicate that credal masking provides principled protection, substantially reducing attack success while yielding fine-tuned privacy-accuracy trade-offs.' volume: 337 URL: https://proceedings.mlr.press/v337/rocchi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/rocchi26a/rocchi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-rocchi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Niccol\textò family: Rocchi - given: Fabio family: Stella - given: Cassio prefix: de family: Campos editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5716-5730 id: rocchi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5716 lastpage: 5730 published: 2026-08-06 00:00:00 +0000 - title: 'Planning with Formal Reachability Guarantees in Goal-Oriented MDPs with Dead-Ends' abstract: 'Goal-oriented {Markov} Decision Processes with unavoidable dead-ends pose a significant challenge to standard planning algorithms, as the goal cannot always be reached with probability $1$. In certain applications, it can be desirable to optimize efficiency only over successful trajectories while enforcing a lower bound on goal reachability, yet no existing method directly addresses this conditional formulation, whose non-linear structure makes direct optimization difficult. To overcome this, we introduce a tractable approximation. Working within an unconstrained utility-maximization framework, we derive an analytical formula that determines a value for the goal-reward parameter sufficient to guarantee that the optimal policy respects the requested reachability threshold. The proposed approach is evaluated on two common benchmark domains, Aircraft Routing and Exploding Blocksworld, and compared against state-of-the-art constrained optimization methods, specifically i-dual and Chance-Constrained. Results show that our method offers a compelling trade-off: it significantly reduces the expected cost compared to conservative lexicographic approaches (i.e. i-dual), while avoiding the failure-seeking bias inherent to methods modelling artificial zero-cost give-up action (i.e. Chance-Constrained).' volume: 337 URL: https://proceedings.mlr.press/v337/roche26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/roche26a/roche26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-roche26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Matisse family: Roche - given: Caroline P.C. family: Chanel - given: Yoko family: Watanabe editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5731-5739 id: roche26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5731 lastpage: 5739 published: 2026-08-06 00:00:00 +0000 - title: 'Constrained Weighted Bayesian Bootstrap' abstract: 'We prove the weighted {Bayesian} bootstrap, a method for approximate sampling of a posterior distribution, can be extended to sample from general constrained posterior distributions under mild assumptions. The method entails a simple algorithm that can take advantage of fast tools from convex optimization. Under regularity conditions, we show the asymptotic distribution of samples from the constrained weighted {Bayesian} bootstrap has a covariance matching the restricted maximum likelihood estimator, an efficient estimator. We assess the method empirically on a variety of constrained {Bayesian} problems, demonstrating broad applicability of the method as well as advantages over existing peer methods. The constrained weighted {Bayesian} bootstrap quickly samples from constrained posteriors, providing adequate uncertainty quantification for problems typically solved via optimization methods designed to deliver only a point estimate. As a case study, using constraints required in European-style option prices, uncertainty estimates of an option pricing surface are derived with constrained weighted {Bayesian} bootstrap.' volume: 337 URL: https://proceedings.mlr.press/v337/rosen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/rosen26a/rosen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-rosen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sam family: Rosen - given: Jason family: Xu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5740-5763 id: rosen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5740 lastpage: 5763 published: 2026-08-06 00:00:00 +0000 - title: 'Kernel Integrated $R^2$: A Measure of Dependence' abstract: 'We introduce kernel integrated $R^2$, a new measure of statistical dependence that combines the local normalization principle of the recently introduced integrated $R^2$ with the flexibility of reproducing kernel {Hilbert} spaces (RKHSs). The proposed measure extends integrated $R^2$ from scalar responses to responses taking values on general spaces equipped with a characteristic kernel, allowing to measure dependence of multivariate, functional, and structured data, while remaining sensitive to tail behaviour and oscillatory dependence structures. We establish that (i) this new measure takes values in $[0,1]$, (ii) equals zero if and only if independence holds, and (iii) equals one if and only if the response is almost surely a measurable function of the covariates. Two estimators are proposed: a graph based method using $K$-nearest neighbours and an RKHS-based method built on conditional mean embeddings. We prove consistency and derive convergence rates for the graph-based estimator, showing its adaptation to intrinsic dimensionality. Numerical experiments on simulated data and a real data experiment in the context of dependency testing for media annotations demonstrate competitive power against state-of-the-art dependence measures, particularly in settings involving non-linear and structured relationships.' volume: 337 URL: https://proceedings.mlr.press/v337/roudaki26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/roudaki26a/roudaki26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-roudaki26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Pouya family: Roudaki - given: Shakeel family: Gavioli-Akilagun - given: Florian family: Kalinke - given: Mona family: Azadkia - given: Zoltán family: Szabó editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5764-5789 id: roudaki26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5764 lastpage: 5789 published: 2026-08-06 00:00:00 +0000 - title: 'VaSST: Variational Inference for Symbolic Regression using Soft Symbolic Trees' abstract: 'Symbolic regression (SR) has gained recent traction in {AI}-driven scientific discovery for learning closed-form physical laws. Yet existing methods are dominated by heuristic search or data-intensive approaches that often assume low-noise regimes and lack principled uncertainty quantification, while fully probabilistic SR formulations remain scarce. We introduce a scalable probabilistic framework for SR, {VaSST}, based on variational inference. {VaSST} uses soft symbolic trees, a continuous relaxation of symbolic expression trees in which discrete operator and feature assignments are replaced by probability distributions over allowable components. This transforms combinatorial symbolic search through an astronomically large expression space into efficient gradient-based optimization while preserving a coherent probabilistic interpretation. The learned soft representations induce posterior distributions over symbolic structures, enabling uncertainty quantification across plausible symbolic forms through posterior-aware symbolic model selection. On simulated experiments and the {Feynman} Symbolic Regression Database, {VaSST} achieves strong structural recovery and predictive accuracy compared to state-of-the-art competing SR methods.' volume: 337 URL: https://proceedings.mlr.press/v337/roy26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/roy26a/roy26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-roy26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Somjit family: Roy - given: Pritam family: Dey - given: Bani family: Mallick editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5790-5844 id: roy26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5790 lastpage: 5844 published: 2026-08-06 00:00:00 +0000 - title: 'Fairness Uncertainty Quantification: A Constrained Stochastic Optimization Perspective' abstract: 'In this paper, we construct confidence interval (CI) for the test-unfairness of a group-fairness aware classifier trained by Stochastic Gradient Descent ({SGD}) type algorithms. Since these algorithms are almost invariably used to train modern machine learning models, the learned parameters—and consequently their fairness—are inherently random. We quantify this randomness, which can have far-reaching consequences, especially for sensitive applications. Viewing fairness-aware classification through the lens of constrained optimization allows us to leverage tools from stochastic approximation theory to establish the asymptotic normality of the estimated parameters. Existing work typically provides fairness guarantees either in expectation or for the exact minimizer of the constrained objective \citep{del2020review, celis2019classification}, without accounting for the stochasticity induced by the optimization algorithm itself. To construct CIs for fairness in practice, we develop an easily parallelizable online multiplier bootstrap procedure. In doing so, we also extend theoretical guarantees for online bootstrap methods from unconstrained {SGD} to the constrained optimization setting which may be of independent interest. We illustrate the effectiveness of our approach through extensive simulations and experiments on benchmark datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/roy26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/roy26b/roy26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-roy26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Abhishek family: Roy - given: Prasant family: Mohapatra editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5845-5865 id: roy26b issued: date-parts: - 2026 - 8 - 6 firstpage: 5845 lastpage: 5865 published: 2026-08-06 00:00:00 +0000 - title: 'Variance Reduction for Non-Log-Concave Sampling with Applications to Inverse Problems' abstract: 'Sampling from high-dimensional, non-log-concave distributions with unnormalized densities is a fundamental challenge in machine learning, particularly when the exact gradient of the potential is unavailable and must be approximated via stochastic gradients that exhibit high variance under a fixed budget of gradient computations per iteration. Although variance reduction techniques such as {SGD} with momentum, STORM, and PAGE have demonstrated improved convergence properties in non-convex optimization, their implications for sampling from non-log-concave distributions remain largely unexplored. In this work, we develop the first unified analysis of these estimators for sampling from non-log-concave distributions. We establish improved non-asymptotic convergence rates in $\varepsilon$-relative {Fisher} information and, under a Poincaré inequality assumption, in squared total variation distance, and further prove weak convergence to the target distribution. We extend our analysis to solving inverse problems with score-based generative priors. We empirically validate our theory and demonstrate that, under a fixed gradient computations per iteration, variance-reduction techniques consistently improve sample quality in two standard imaging applications.' volume: 337 URL: https://proceedings.mlr.press/v337/sahin26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sahin26a/sahin26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sahin26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: M. Berk family: Sahin - given: Ahmet Ege family: Tanriverdi - given: Behzad family: Sharif - given: Abolfazl family: Hashemi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5866-5918 id: sahin26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5866 lastpage: 5918 published: 2026-08-06 00:00:00 +0000 - title: 'Bayesian Adaptation Gym: A Benchmark for the Bayesian Low-Rank Adaptation of Multi-Modal Language Models' abstract: 'Large multi-modal language models are increasingly deployed in high-stakes domains, making well-calibrated uncertainty essential. Traditional {Bayesian} methods approximate posteriors over all model weights, which becomes intractable for modern large models. For this reason, recent work instead considers {Bayesian} low-rank adaptation to enable tractable posterior approximation. Due to a lack of a standardized benchmark to evaluate these approaches, it remains unclear where these methods provide meaningful benefits. To fill this gap, we introduce {Bayesian} Adaptation Gym (BAG), a benchmark for the {Bayesian} adaptation of multi-modal language models. BAG provides reference implementations of classic {Bayesian} baselines and state-of-the-art adaptation methods, along with a multi-modal dataset and task suite designed to probe calibration, robustness under distribution shift, and decision-making under uncertainty via active learning. Using BAG, we conduct and report extensive experiments across model sizes, datasets, and tasks to highlight the successes and failures of current {Bayesian} adaptation approaches. To enable further research, BAG is fully open source: https://github.com/SRI-CSL/BayesAdapt.' volume: 337 URL: https://proceedings.mlr.press/v337/samplawski26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/samplawski26a/samplawski26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-samplawski26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Colin family: Samplawski - given: Ramneet family: Kaur - given: Manoj family: Acharya - given: Anirban family: Roy - given: Adam D. family: Cobb editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5919-5966 id: samplawski26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5919 lastpage: 5966 published: 2026-08-06 00:00:00 +0000 - title: 'Quantized Stochastic Primal–Dual Methods for Distributed Optimization under Relaxed Global Geometry' abstract: 'We study distributed optimization with stochastic gradients and finite-bit communication modeled by random (unbiased) quantization. We propose q-PDGD, a quantized stochastic primal–dual method, and analyze it under relaxed global geometry. Under restricted secant inequality (RSI), a constant step-size yields linear contraction to an explicit neighborhood determined by gradient noise, quantization distortion, and network connectivity, while a diminishing step-size achieves $\mathcal{O}(1/k)$ convergence without shared-minimizer assumptions. Under Polyak–{Ł}ojasiewicz (PL) inequality, we obtain linear-to-neighborhood convergence in the same stochastic quantized setting. Our results match the best-known centralized stochastic rates in oracle complexity, and are supported by experiments demonstrating the predicted tradeoffs between quantization level, step-size choice, and graph structure.' volume: 337 URL: https://proceedings.mlr.press/v337/sarkar26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sarkar26a/sarkar26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sarkar26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Susmit family: Sarkar - given: Abhinav family: Raghuvanshi - given: Kushal family: Chakrabarti - given: Mayank family: Baranwal editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5967-5996 id: sarkar26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5967 lastpage: 5996 published: 2026-08-06 00:00:00 +0000 - title: 'Global Convergence of Average Reward Constrained MDPs with Neural Critic and General Policy Parameterization' abstract: 'We study infinite-horizon Constrained {Markov} Decision Processes (CMDPs) with general policy parameterizations and multi-layer neural network critics. Existing theoretical analyses for constrained reinforcement learning largely rely on tabular policies or linear critics, which limits their applicability to high-dimensional and continuous control problems. We propose a primal–dual natural actor–critic algorithm that integrates neural critic estimation with natural policy gradient updates and leverages Neural Tangent Kernel ({NTK}) theory to control function-approximation error under Markovian sampling, without requiring access to mixing-time oracles. We establish global convergence and cumulative constraint violation rates of $\tilde{\mathcal{O}}(T^{-1/4})$ up to approximation errors induced by the policy and critic classes. Our results provide the first such guarantees for CMDPs with general policies and multi-layer neural critics, substantially extending the theoretical foundations of actor–critic methods beyond the linear-critic regime.' volume: 337 URL: https://proceedings.mlr.press/v337/satheesh26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/satheesh26a/satheesh26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-satheesh26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Anirudh family: Satheesh - given: Pankaj Kumar family: Barman - given: Washim Uddin family: Mondal - given: Vaneet family: Aggarwal editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 5997-6025 id: satheesh26a issued: date-parts: - 2026 - 8 - 6 firstpage: 5997 lastpage: 6025 published: 2026-08-06 00:00:00 +0000 - title: 'A Sobering Look at Tabular Data Generation via Probabilistic Circuits' abstract: 'Tabular data is more challenging to generate than text and images, due to its heterogeneous features and much lower sample sizes. On this task, diffusion-based models are the current state-of-the-art (SotA) model class, achieving almost perfect performance on commonly used benchmarks. In this paper, we question the perception of progress for tabular data generation. First, we highlight the limitations of current protocols to evaluate the fidelity of generated data, and advocate for alternative ones. Next, we revisit a simple baseline—hierarchical mixture models in the form of deep probabilistic circuits (PCs)—which delivers competitive or superior performance to SotA models for a fraction of the cost. PCs are the generative counterpart of decision forests, and as such can natively handle heterogeneous data as well as deliver tractable probabilistic generation and inference. Finally, in a rigorous empirical analysis we show that the apparent saturation of progress for SotA models is largely due to the use of inadequate metrics. As such, we highlight that there is still much to be done to generate realistic tabular data.' volume: 337 URL: https://proceedings.mlr.press/v337/scassola26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/scassola26a/scassola26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-scassola26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Davide family: Scassola - given: Dylan family: Ponsford - given: Adrián family: Javaloy - given: Sebastiano family: Saccani - given: Luca family: Bortolussi - given: Henry family: Gouk - given: Antonio family: Vergari editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6026-6063 id: scassola26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6026 lastpage: 6063 published: 2026-08-06 00:00:00 +0000 - title: 'The Price of Knowledge: Optimal Algorithms for Costly Bandits' abstract: 'We study stochastic bandits in which observing a reward is optional but incurs an action-dependent cost. This setting captures applications where feedback acquisition (e.g., human evaluation or randomized testing) is expensive, and the learner must trade off exploration, exploitation, and observation cost. We formulate regret to include both reward loss and the cumulative cost of requested observations. Our first result is structural: for minimizing regret, it is without loss of generality to consider two-phase policies that first request labels during an exploration phase and then commit to a single action without further observations. Building on this reduction, we introduce two cost-sensitive complexity measures that extend maximum information gain: a cost-adjusted information gain $\Gamma_T(c)$ for minimax analysis, and a cost- and gap-adjusted information gain $\Gamma_T^{\mathrm{gap}}(\Delta_c)$ for instance-dependent analysis. Using these quantities, we develop two {Gaussian}-process-based algorithms, C3-GP and GP-C-LUCB, and derive regret upper bounds for correlated-action settings with heterogeneous observation costs. In the finite independent-arm setting, we further prove matching lower and upper bounds (up to constants/logarithmic factors), yielding a tight characterization of both minimax and instance-dependent regret in terms of the proposed cost-aware complexity measures.' volume: 337 URL: https://proceedings.mlr.press/v337/schur26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/schur26a/schur26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-schur26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Felix family: Schur - given: Jesus family: Lago - given: Tanner family: Fiez editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6064-6090 id: schur26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6064 lastpage: 6090 published: 2026-08-06 00:00:00 +0000 - title: 'Sign Identifiability of Causal Effects in Stationary Stochastic Dynamical Systems' abstract: 'We study identifiability in continuous-time linear stationary stochastic differential equations with a known causal structure. Unlike existing approaches, we relax the assumption of a known diffusion matrix, thereby respecting the model’s intrinsic scale invariance. Therefore, rather than recovering drift coefficients themselves, we introduce edge-sign identifiability: for a given causal structure, we ask whether the sign of a given drift entry is uniquely determined across all observational covariance matrices induced by parametrisations compatible with that structure. This leads to a trichotomy of edge-sign identifiability: identifiable, non-identifiable, and partially identifiable. This trichotomy introduces the new notion of partial identifiability to the literature, which we show is a genuine category in our setting. Under a notion of faithfulness, we derive criteria to identify membership of each category for general graphs. Applying our criteria to specific causal structures, both analogous to classical causal settings (e.g., instrumental variables) and novel cyclic settings, we determine their edge-sign identifiability and, in some cases, obtain explicit expressions for the sign of a target edge in terms of the observational covariance matrix.' volume: 337 URL: https://proceedings.mlr.press/v337/seeventer26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/seeventer26a/seeventer26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-seeventer26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Gijs prefix: van family: Seeventer - given: Saber family: Salehkaleybar editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6091-6124 id: seeventer26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6091 lastpage: 6124 published: 2026-08-06 00:00:00 +0000 - title: 'Birds of a Feather Reason Together: Gestalt Grouping Meets Neuro-Symbolic Inference' abstract: 'This paper introduces Gestalt Reasoning Machines (GRMs), a novel neuro-symbolic framework that integrates Gestalt principles to enhance reasoning models with perception capabilities similar to human cognition. Traditional models, which rely on large datasets and complex computations, often overlook the crucial human cognitive function of grouping, resulting in inefficiencies when dealing with abstract concepts. GRMs address this challenge by incorporating a grouping mechanism grounded in Gestalt principles, enabling the system to recognize and reason over complex visual patterns that are otherwise difficult to capture through object-level features alone. This grouping capability allows GRMs to identify higher-order structures and relational configurations that are essential for human-like reasoning. We demonstrate that GRMs outperform purely neural baselines by leveraging logic-based reasoning infused with perceptual grouping cues, offering a more interpretable and cognitively aligned approach. Our contributions include the design of GRMs and the empirical validation of their effectiveness in visual reasoning tasks that demand structured perception.' volume: 337 URL: https://proceedings.mlr.press/v337/sha26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sha26a/sha26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sha26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jingyuan family: Sha - given: Hikaru family: Shindo - given: Kristian family: Kersting - given: Devendra Singh family: Dhami editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6125-6148 id: sha26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6125 lastpage: 6148 published: 2026-08-06 00:00:00 +0000 - title: 'The Art of Calling the Winner by Asking Just Enough Questions' abstract: 'We study active elicitation of agent preferences for collectively choosing among $m$ alternatives using prominent voting rules. We focus on the next-best query model, in which an agent responds to a query by revealing their next most favorite alternative, and measure the competitive ratio, which is the worst case ratio between the number of queries made by the active elicitation algorithm and the minimum number of queries needed to reveal the winning alternative(s) in hindsight. We show that the best competitive ratio is sublinear in $m$ for many positional scoring rules but linear in $m$ for all Condorcet-consistent rules. Our analysis centers on a simple elicitation algorithm we propose, which not only achieves optimal theoretical bounds, but also impressive empirical performance on real data.' volume: 337 URL: https://proceedings.mlr.press/v337/shah26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/shah26a/shah26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-shah26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nisarg family: Shah - given: Ziqi family: Yu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6149-6164 id: shah26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6149 lastpage: 6164 published: 2026-08-06 00:00:00 +0000 - title: 'Analytic Planning under Uncertainty with Moment Closure' abstract: 'Effective model-based reinforcement learning in stochastic environments requires planning that accounts for predictive uncertainty. Propagating full state distributions analytically offers a principled way to do this, but has traditionally required restrictive policy or reward structures to remain tractable. Consequently, modern deep reinforcement learning has largely retreated to either stochastic sampling, which introduces significant target variance, or deterministic point estimates that ignore predictive covariance entirely. We investigate whether distribution-aware planning is possible without these constraints. Using a quadratic action-value parameterization, we first reduce the {Bellman} backup to an expectation over the state-value function alone; the key idea is then a compatibility principle between the predictive transition distribution and the value function class, under which this expectation is analytic in the distribution’s moments. We instantiate this principle with a {Gaussian} transition model paired with a radial-basis value function, yielding a closed-form backup that propagates both predictive mean and covariance. Empirically, our approach reduces target variance and yields well-calibrated predictive uncertainty under stochastic observations in continuous control, providing a principled framework for planning with learned distribution models.' volume: 337 URL: https://proceedings.mlr.press/v337/sharma26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sharma26a/sharma26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sharma26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shishir family: Sharma - given: Doina family: Precup editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6165-6177 id: sharma26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6165 lastpage: 6177 published: 2026-08-06 00:00:00 +0000 - title: 'Improving TensorSketch Using Complex Random Variables' abstract: '$\texttt{{TensorSketch}}$ by [Pham and Pagh, 2013, Kar and Karnick, 2012] provides efficient sketching algorithms for high-dimensional polynomial kernels $\mathbf{x}^{\otimes p} \in \mathbb{R}^{d^p}$. [Kar and Karnick, 2012] uses dense Johnson-Lindenstrauss (JL)-type projections with computational cost $O(pDd)$, whereas [Pham and Pagh, 2013] extends the sparse $\texttt{CountSketch}$ [Charikar et al., 2004] algorithm, yielding a faster algorithm for high-dimensional sparse inputs with running time $O\big(p(\operatorname{nnz}(\mathbf{x}) + D \log D)\big)$. However, the variance of both estimators grows exponentially with the polynomial degree $p$, scaling as $3^{p}/D$, where $D$ denotes the sketch dimension. Recent work by [Wacker et al., 2023] showed that using complex-valued distribution reduces this dependence to $2^{p}/D$ for the approach of [Kar and Karnick, 2012]. However, their method relies on dense JL-type projections with computational cost $O(pDd)$ and does not extend to the algorithm of [Pham and Pagh, 2013]. In this work, we introduce a simple variant of $\texttt{{TensorSketch}}$ [Pham and Pagh, 2013] that achieves the same variance bound as [Wacker et al., 2023], while retaining its advantage of the input-sparsity running time. We validate our results with supporting experiments on synthetic and real-world datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/sharma26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sharma26b/sharma26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sharma26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Amit family: Sharma - given: Mohammad Azhar family: Khan - given: Rameshwar family: Pratap - given: Keegan family: Kang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6178-6203 id: sharma26b issued: date-parts: - 2026 - 8 - 6 firstpage: 6178 lastpage: 6203 published: 2026-08-06 00:00:00 +0000 - title: 'Finding the Signal in the Spam: Jointly Learning Rewards and Worker Reliability from Pairwise Comparisons' abstract: 'The problem of learning from pairwise comparisons has been widely studied across many domains such as recommendation systems, social choice, and more recently, fine-tuning large language models. In this problem, the goal is to learn item rewards based on pairwise comparisons between them. In many scenarios, these comparisons are elicited from crowdworkers using platforms such as Amazon Mechanical Turk, Scale {AI}, etc. However, crowdworkers are often unreliable due to limited domain knowledge or revenue-maximizing (spamming) behavior. In this work, our goal is to understand whether worker reliability (competency) can be learned jointly with item rewards. To this end, we adopt the Boltzmann-rational model for pairwise comparisons, which extends the Bradley–Terry–Luce model by incorporating worker competencies. We derive an EM-based algorithm for learning under this model by introducing Polya-Gamma latent variables to transform the logistic likelihood into a conditionally {Gaussian} form, enabling tractable optimization and leading to a simplified $Q$ function in the E-step of the algorithm. This technique allows us to reduce our formulation to a matrix sensing problem, using which we establish theoretical convergence guarantees for our algorithm. We conduct extensive experiments on real-world and synthetic datasets. These experiments demonstrate the advantages of using our algorithm over several baselines and confirm its strong robustness to both spammers and adversarial workers, highlighting its practical effectiveness in realistic crowdsourcing and reward learning settings.' volume: 337 URL: https://proceedings.mlr.press/v337/shejole26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/shejole26a/shejole26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-shejole26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kaustubh Shivshankar family: Shejole - given: Tanish family: Agarwal - given: Arpit family: Agarwal - given: Avishek family: Ghosh editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6204-6231 id: shejole26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6204 lastpage: 6231 published: 2026-08-06 00:00:00 +0000 - title: 'Valid and Efficient Uncertainty Quantification for Federated Joint Shift' abstract: 'Reliable uncertainty quantification (UQ) is critical for safety-sensitive federated learning (FL) applications, such as cross-hospital diagnosis and global sensor networks. In FL, privacy constraints prevent centralized data pooling, while client data exhibit joint distribution shifts across covariates, labels, and conditionals. These shifts violate the exchangeability assumption required by conformal prediction ({CP}), which otherwise guarantees distribution-free coverage under i.i.d. data. To address this gap, we propose Federated Conformal Prediction for Joint Shift (FCPJS), enabling valid {CP} under heterogeneous clients without sharing raw data. Specifically, the method operates in two stages: (i) the server constructs a privacy-preserving global sketch of nonconformity score distributions; (ii) each client performs importance-weighted calibration by contrasting its local scores with the global sketch. This distribution-ratio weighting corrects joint shifts in a unified manner. We prove that FCPJS attains valid marginal coverage across clients, up to an $O(\sqrt{\varepsilon_m}+1/\sqrt{n})$ error from the finite number of calibration samples $n$ and sketch size $m$. Experiments on four heterogeneous benchmarks show that \newCP{} preserves coverage and improves predictive efficiency by $12.64%$ over the strongest baseline. To our knowledge, FCPJS is the first method providing provably valid and efficient conformal UQ for FL under joint distribution shift.' volume: 337 URL: https://proceedings.mlr.press/v337/shi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/shi26a/shi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-shi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuanjie family: Shi - given: Peihong family: Li - given: Xuanyu family: Cao - given: Yan family: Yan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6232-6260 id: shi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6232 lastpage: 6260 published: 2026-08-06 00:00:00 +0000 - title: 'Evaluation of "Probabilities of Causation" in Case-Control Studies: Identification and Estimation' abstract: '"Probabilities of causation" play a crucial role in practical science. {Pearl} [2009] defined three types of probabilities of causation in the context of structural causal models: the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Furthermore, Tian and {Pearl} [2000] and Kuroki and Cai [2011] provided the identification conditions for these probabilities under the assumption of monotonicity. However, these identification conditions are described based on "the joint probabilities of observed probabilities" and/or "causal risks". Therefore, they are not applicable to case–control studies, in which the available statistical data are given in the form of the conditional probabilities of observed variables given an outcome variable. To address this limitation, this paper provides novel identification conditions for the probabilities of causation using (i) two proxy covariates and (ii) a proxy covariate together with an instrumental variable. Remarkably, the use of a proxy covariate and an instrumental variable enables the identification not only of the probabilities of causation but also of the joint distribution of the potential outcome variables. When these probabilities can be evaluated using the proposed identification conditions, new plug-in estimators of these probabilities are presented.' volume: 337 URL: https://proceedings.mlr.press/v337/shingaki26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/shingaki26a/shingaki26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-shingaki26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ryusei family: Shingaki - given: Haruka family: Yoshida - given: Manabu family: Kuroki editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6261-6282 id: shingaki26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6261 lastpage: 6282 published: 2026-08-06 00:00:00 +0000 - title: 'Fixed-Confidence Best-Arm Identification for Causal Mediation Analysis' abstract: 'This paper studies the problem of identifying the treatment that maximizes the expected natural direct potential outcome (NDPO), which captures the potential outcome of an intervention while excluding the pathway transmitted through a mediator that researchers may wish to remove from evaluation. We first establish population-level identification of the expected NDPO in a causal bandit setting using observable interventional distributions. We then develop a fixed-confidence best-arm identification (BAI) algorithm based on the Track-and-Stop (TaS) framework, employing a cutting-set method to solve the resulting semi-infinite optimization problem. The proposed algorithm achieves sample-efficient identification with a high-probability correctness guarantee. We prove that it satisfies $\delta$-correctness and asymptotic optimality. Finally, we validate the approach through empirical evaluations on a large-scale real-world advertising dataset (IPinYou).' volume: 337 URL: https://proceedings.mlr.press/v337/shrivastava26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/shrivastava26a/shrivastava26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-shrivastava26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Harsh family: Shrivastava - given: Yuta family: Kawakami - given: Junpei family: Komiyama - given: Jin family: Tian editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6283-6309 id: shrivastava26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6283 lastpage: 6309 published: 2026-08-06 00:00:00 +0000 - title: 'Collaborative Multi-view Learning from Crowds' abstract: 'As an effective post-processing approach to improving the quality of integrated labels, noise correction has received extensive attention in recent years. Recent studies have shown that utilizing information from both the original attribute view and the multiple noisy label view can significantly improve the performance of noise correction. However, most existing algorithms often learn information independently on each view, making them difficult to fully exploit the complementary information between these two views. To address this limitation, we propose a noise correction algorithm called collaborative multi-view learning from crowds (CMLFC). CMLFC first constructs instance correlation graphs on the original attribute view and the multiple noisy label view, respectively, and designs dedicated encoders to obtain view-specific representations. To capture the deep complementary information between these two views, it designs a contrastive fusion encoder to distill common representations from these two view-specific representations, and then forms a common view. Next, it trains three view-specific classifiers on these three views, and designs a joint loss function to collaboratively train these encoders and classifiers, enabling information to flow bidirectionally among views, thereby improving the quality of representations in each view. Finally, it employs the trained view-specific encoders and classifiers to obtain each instance’s representations and class probability distributions, respectively, which are then used to update its integrated label. Extensive experiments on real-world crowdsourced datasets validate the effectiveness, ablation, and sensitivity of CMLFC. Our codes and datasets are available at https://github.com/jiangliangxiao/CMLFC.' volume: 337 URL: https://proceedings.mlr.press/v337/si26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/si26a/si26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-si26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shanshan family: Si - given: Liangxiao family: Jiang - given: Wenjun family: Zhang - given: Chaoqun family: Li - given: Liangjun family: Yu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6310-6320 id: si26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6310 lastpage: 6320 published: 2026-08-06 00:00:00 +0000 - title: 'Conditional neural control variates for variance reduction in Bayesian inverse problems' abstract: '{Bayesian} inference for inverse problems involves computing expectations under posterior distributions–e.g., posterior means, variances, or predictive quantities–typically via Monte Carlo (MC) estimation. When the quantity of interest varies significantly under the posterior, accurate estimates demand many samples–a cost often prohibitive for partial differential equation-constrained problems. To address this challenge, we introduce conditional neural control variates, a modular method that learns amortized control variates from joint model-data samples to reduce the variance of MC estimators. To scale to high-dimensional problems, we leverage {Stein}’s identity to design an architecture based on an ensemble of hierarchical coupling layers with tractable Jacobian trace computation. Training requires: (i) samples from the joint distribution of unknown parameters and observed data; and (ii) the posterior score function, which can be computed from physics-based likelihood evaluations, neural operator surrogates, or learned generative models such as conditional normalizing flows. Once trained, the control variates generalize across observations without retraining. We validate our approach on stylized and partial differential equation-constrained Darcy flow inverse problems, outperforming classical {Stein} control variates and achieving substantial variance reduction, even when the analytical score is replaced by a learned surrogate.' volume: 337 URL: https://proceedings.mlr.press/v337/siahkoohi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/siahkoohi26a/siahkoohi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-siahkoohi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ali family: Siahkoohi - given: Hyunwoo family: Oh editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6321-6341 id: siahkoohi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6321 lastpage: 6341 published: 2026-08-06 00:00:00 +0000 - title: 'A Stronger Calculus of Intervention for Max-Linear Bayesian Networks' abstract: 'Max-linear {Bayesian} networks (MLBNs) are a novel class of directed acyclic graphical models which are of interest to statistics and data science due to their relevance to causality and probabilistic inference, particularly of extreme events. Interestingly, MLBNs encode strictly more conditional independence than general structural causal models. Because of this, MLBNs are {Markov} to a strengthening of the $d$-separation criterion called $\ast$-separation. As many tools for causal inference (most notably, Judea {Pearl}’s $do$-calculus) are based on $d$-separation, we address the natural question of whether assuming Markovianity to $\ast$-separation can lead to additional causal effect identifiability under intervention. We answer this question in the affirmative and develop a stronger version of the $do$-calculus rules for models which are {Markov} to $\ast$-separation. However, we note that restrictions inherent to the max-linear setting (in particular, that they give rise to non strictly positive joint probability distributions) mean that our calculus is only applicable to specific kinds of policy intervention.' volume: 337 URL: https://proceedings.mlr.press/v337/sierau26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sierau26a/sierau26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sierau26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Leon family: Sierau - given: Francesco family: Nowell - given: Nihat family: Ay editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6342-6365 id: sierau26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6342 lastpage: 6365 published: 2026-08-06 00:00:00 +0000 - title: 'Particle GFlowNets: Rethinking Generative Marginalization Models' abstract: 'Generative Marginalization Models (MaMs) have been recently introduced as efficient neural sampling models for any-order autoregressive modelling of discrete distributions. By learning both the marginal and conditional probabilities of a persistent-block {Gibbs} sampler, MaMs enable fast posterior evaluation with a single neural network forward pass. While prior work has considered MaMs to be distinct from Generative Flow Networks ({GFlowNets}), a well-established paradigm for inference in discrete stochastic models, we show that they are equivalent. Then, we also extend MaMs’ sampling strategy to non-autoregressive generative processes. In particular, we describe an automatic criterion for full-state rejuvenation of the {Gibbs} sampler, derived from the Gelman-Rubin statistic, which plays a key role in speeding up learning convergence. Our experiments show that our method, called Particle {GFlowNets}, markedly accelerates training in large combinatorial spaces.' volume: 337 URL: https://proceedings.mlr.press/v337/silva26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/silva26a/silva26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-silva26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tiago prefix: da family: Silva - given: Diego family: Mesquita - given: Salem family: Lahlou editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6366-6383 id: silva26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6366 lastpage: 6383 published: 2026-08-06 00:00:00 +0000 - title: 'The Minimal Search Space for Conditional Causal Bandits' abstract: 'Causal knowledge can be used to support decision-making problems. This has been recognized in the causal bandits literature, where a causal (multi-armed) bandit is characterized by a causal graphical model and a target variable. The arms are then interventions on the causal model, and rewards are samples of the target variable. Causal bandits were originally studied with a focus on hard interventions. We focus instead on cases where the arms are conditional interventions, which more accurately model many real-world decision-making problems by allowing the value of the intervened variable to be chosen based on the observed values of other variables. This paper presents a graphical characterization of the minimal set of nodes guaranteed to contain the optimal conditional intervention, which maximizes the expected reward. We then propose an efficient algorithm with a time complexity of $O(|V| + |E|)$ to identify this minimal set of nodes. We prove that the graphical characterization and the proposed algorithm are correct. Finally, we empirically demonstrate that our algorithm significantly prunes the search space and substantially accelerates convergence rates when integrated into standard multi-armed bandit algorithms.' volume: 337 URL: https://proceedings.mlr.press/v337/simoes26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/simoes26a/simoes26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-simoes26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Francisco N. F. Q. family: Simoes - given: Itai family: Feigenbaum - given: Mehdi family: Dastani - given: Thijs prefix: van family: Ommen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6384-6409 id: simoes26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6384 lastpage: 6409 published: 2026-08-06 00:00:00 +0000 - title: 'Learning-based Optimal Admission Control for Erlang-B Queuing Systems' abstract: 'This paper studies a learning-based optimal admission control policy for an Erlang–B queuing system under partial observation. Only at each arrival, the dispatcher observes the current occupancy and decides whether to accept or reject the job. A completed job yields a fixed reward but incurs a cost proportional to the service duration. The objective is to design an admission control policy that maximizes the long-term average reward. The arrival and service rates are unknown, and unobserved departures complicate parameter estimation. The reward structure induces an asymmetry in the optimal decision across parameter regimes. We establish an instance-dependent asymptotic lower bound, explicitly dependent on the system parameters, demonstrating that the worst-case regret is logarithmic in the number of arrivals in one regime.' volume: 337 URL: https://proceedings.mlr.press/v337/singh26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/singh26a/singh26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-singh26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shubhhi family: Singh - given: Shubhanshu family: Shekhar - given: Vijay G family: Subramanian editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6410-6444 id: singh26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6410 lastpage: 6444 published: 2026-08-06 00:00:00 +0000 - title: 'Consensus Optimization Graph Neural Networks' abstract: 'Implicit graph neural networks (GNNs) cast inference as optimization, computing node embeddings as the solution to a graph-structured optimization problem. By coupling node embeddings through a shared global objective, implicit GNNs naturally capture long-range dependencies, addressing a key limitation of standard message-passing GNNs. Another appealing property of these models is that inference can be performed in a decentralized and asynchronous manner, making them well suited for deployment in multi-agent systems. However, training is costly, as it requires solving optimization problems in both the forward and backward pass. In this work, we focus on graph-level prediction and introduce an approach for directly computing graph-level representations in implicit GNNs that bypasses the need for node embeddings. We do this by reformulating the internal optimization problem to operate over a shared graph embedding. This significantly reduces both computation and memory costs, while retaining compatibility with decentralized and asynchronous inference. Experiments across multiple benchmarks show that the shared-embedding approach consistently matches the predictive performance of using node embeddings, providing a simpler and more efficient alternative for graph-level tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/solodova26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/solodova26a/solodova26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-solodova26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Olga family: Solodova - given: Ryan P family: Adams editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6445-6466 id: solodova26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6445 lastpage: 6466 published: 2026-08-06 00:00:00 +0000 - title: 'Adaptive Fourier Decomposition-guided Neural Operator Design for Inverse PDE Problems' abstract: 'Inverse problems, which are generally ill-posed, aim to identify the unknown parameters of a physical system from the observations of its output. A large class of inverse problems for partial differential equations (PDEs) are only well-defined as mappings from operators to functions. However, existing operator learning frameworks either do not explicitly account for the underlying operator space or solve the inverse problems in a {Hilbert} space. Meanwhile, it has been shown that a Banach space setting for the parameter space would be closer to reality for a wide range of problems. Driven by this, we introduce AFDONet-inv, a novel neural operator solver whose design is rigorously guided by adaptive {Fourier} decomposition (AFD) theory, to solve inverse problems for PDEs in a Banach space. Each component of AFDONet-inv’s architecture, including primal and dual nets, latent-to-RKBS (reproducing kernel Banach space) network, and dynamic convolutional kernel network (CKN), has a corresponding component in the AFD operation in Banach space. This way, AFDONet-inv is mathematically explainable and grounded in the AFD theory and possesses several desirable properties. Extensive experiments demonstrate that AFDONet-inv outperforms state-of-the-art inverse {PDE} solvers in terms of solution accuracy.' volume: 337 URL: https://proceedings.mlr.press/v337/song26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/song26a/song26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-song26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zeyuan family: Song - given: Xiaocong family: Zhen - given: Zheyu family: Jiang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6467-6491 id: song26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6467 lastpage: 6491 published: 2026-08-06 00:00:00 +0000 - title: 'Privacy-Preserving Robustness Verification for Neural Networks' abstract: 'Neural network verification and data privacy are inherently in tension: verification demands full access to model parameters and input data, yet both are increasingly restricted by privacy regulations and intellectual property constraints. This tension has left robustness verification impractical in privacy-sensitive domains. In this work, we address this gap with SecureCROWN, the first framework for privacy-preserving neural network robustness verification. Built upon secure two-party computation (2PC), our framework enables a model owner and a data owner to jointly compute certified robustness bounds—revealing only the final result while provably protecting both parties’ private data under the semi-honest security model. A key challenge is securely computing the conditional operations in Linear Bound Propagation, where the data-dependent branching is incompatible with standard secure computation protocols. We eliminate branching by formulating conditional logic as continuous arithmetic operations. Additionally, we introduce a Newton–Raphson refinement method to improve numerical stability. Extensive analysis and experiments show that SecureCROWN strictly matches plaintext verification results, while completing in 0.1–200s across varied model sizes and communication settings (LAN/WAN), demonstrating the feasibility of privacy-preserving neural network verification.' volume: 337 URL: https://proceedings.mlr.press/v337/song26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/song26b/song26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-song26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nianyun family: Song - given: Xiaokun family: Luan - given: Yu family: Guo - given: Rongfang family: Bie - given: Meng family: Sun - given: Xiyue family: Zhang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6492-6511 id: song26b issued: date-parts: - 2026 - 8 - 6 firstpage: 6492 lastpage: 6511 published: 2026-08-06 00:00:00 +0000 - title: 'Multiwinner Voting with Interval Preferences under Incomplete Information' abstract: 'In multiwinner approval elections with many candidates, voters may struggle to determine their preferences over the entire slate of candidates. It is therefore of interest to explore which (if any) fairness guarantees can be provided under reduced communication. In this paper, we consider voters with one-dimensional preferences: voters and candidates are associated with points in $\mathbb R$, and each voter’s approval set forms an interval of $\mathbb R$. We put forward a probabilistic preference model, where the voter set consists of different groups; each group is associated with a distribution over an interval of $\mathbb R$, so that each voter draws the endpoints of her approval interval from the distribution associated with her group. We present an algorithm for computing committees that provide Proportional Justified Representation + (PJR+), which proceeds by querying voters’ preferences, and show that, in expectation, it makes $\mathcal{O}(\log k)$ queries per voter, where $k$ is the desired committee size.' volume: 337 URL: https://proceedings.mlr.press/v337/springham26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/springham26a/springham26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-springham26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Drew family: Springham - given: Edith family: Elkind - given: Bart family: De Keijzer - given: Maria family: Polukarov editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6512-6536 id: springham26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6512 lastpage: 6536 published: 2026-08-06 00:00:00 +0000 - title: 'Possibilistic Instrumental Variable Regression with Potentially Invalid Instruments' abstract: 'Instrumental variable regression is a common approach for causal inference in the presence of unobserved confounding. However, identifying valid instruments is often difficult in practice. In this paper, we propose a novel method based on possibility theory that performs posterior inference on the treatment effect, conditional on a user-specified set of potential violations of the instrument exogeneity assumption. Our method can provide valid results even when only a single, potentially invalid, instrument is available. Crucially, and in contrast with existing methods, we prove a finite-sample coverage guarantee for the exactly calibrated (validified) uncertainty intervals when the violation set contains the true value, and we provide practical MC/$\chi^2$ approximations. Simulation experiments and real-data applications indicate strong performance of the proposed approach.' volume: 337 URL: https://proceedings.mlr.press/v337/steiner26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/steiner26a/steiner26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-steiner26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Gregor family: Steiner - given: Jeremie family: Houssineau - given: Mark family: Steel editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6537-6553 id: steiner26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6537 lastpage: 6553 published: 2026-08-06 00:00:00 +0000 - title: 'Classical and Quantum Speedups for Non-Convex Optimization via Energy Conserving Descent' abstract: 'We present the first analytical study of ECD, focusing on the one-dimensional setting for this first installment. We formalize a stochastic ECD dynamics (sECD) with energy-preserving noise, as well as a quantum analog of the ECD Hamiltonian (qECD), providing the foundation for a quantum algorithm through Hamiltonian simulation in a tractable model where the barrier-crossing mechanism can be computed explicitly. For one-dimensional double-well objectives in the under-guessing regime, we compute the expected dynamical hitting times from a local minimum to the global minimum. We prove that both sECD and qECD exhibit exponential improvements in continuous hitting time relative to their respective gradient-based baselines, stochastic gradient descent ({SGD}) and quantum tunneling walk (QTW). For objectives with tall barriers, qECD admits a further hitting time improvement over sECD. Mechanistically, ECD sidesteps the exponential cost associated with rare-escape events of {SGD} from local minima by moving from dissipative to energy-conserving dynamics.' volume: 337 URL: https://proceedings.mlr.press/v337/sun26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sun26a/sun26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sun26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yihang family: Sun - given: Huaijin family: Wang - given: Patrick family: Hayden - given: Jose family: Blanchet editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6554-6575 id: sun26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6554 lastpage: 6575 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Who to Treat When Treatment is Missing' abstract: 'Policy learning methods are increasingly used to inform treatment allocation under budget constraints. Most proposed methods assume complete treatment data, yet applications frequently suffer from missingness that can bias estimates and lead to suboptimal policies. We address this gap by extending efficient estimators for average treatment effect ({ATE}) estimation to policy value and conditional average treatment effect (CATE) estimation under missing at random (MAR) and missing completely conditionally at random (MCCAR) treatment data. Through asymptotic efficiency analysis, we prove that the MAR estimator, which leverages partially-observed units, is both valid and more efficient than the MCCAR estimator when MCCAR assumptions hold. This result provides formal justification for preferring MAR-based estimation in policy learning under both missing data settings. Our comprehensive experiments using synthetic and semi-synthetic datasets confirm that correctly specifying the missingness mechanism is crucial: misspecified estimators remain biased regardless of sample size, while our estimators achieve near-oracle performance when assumptions are satisfied. Our work provides practitioners with theoretically grounded, empirically validated tools for robust policy learning in the presence of missing treatment data.' volume: 337 URL: https://proceedings.mlr.press/v337/sundberg26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/sundberg26a/sundberg26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-sundberg26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Johnna family: Sundberg - given: Rayid family: Ghani - given: Eli family: Ben-Michael - given: Edward family: Kennedy editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6576-6609 id: sundberg26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6576 lastpage: 6609 published: 2026-08-06 00:00:00 +0000 - title: 'Deep Spectral Learning of Embedded Latent Transfer Operators for Stochastic Dynamical Systems' abstract: 'We propose a spectral learning method for stochastic nonlinear dynamical systems represented with embedded latent transfer operators in deep feature spaces. We instantiate the method as Deep Spectral Encoder (DSE), an operator-based latent state-space model in which a time-invariant neural encoder implements learnable nonlinear feature maps from observations, and these features define Markovian latent states whose temporal evolution and observation mapping are described by the transfer and observation operators, respectively. Functional canonical correlation analysis in a learnable Galerkin-projected feature space provides state coordinates from past and future observations, and the two linear operators are estimated on the state coordinates as ridge-regularized closed-form solutions that coincide with Galerkin projections of the associated covariance operators. On this representation, we generalize sequential {Bayesian} filtering and {Koopman} spectral mode decomposition in feature space. Experiments on several scenarios show stable and superior performance with sequential {Bayesian} filtering and dynamic mode decomposition baselines even under noise and partial observability.' volume: 337 URL: https://proceedings.mlr.press/v337/tanaka26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/tanaka26a/tanaka26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-tanaka26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ryogo family: Tanaka - given: Yoshinobu family: Kawahara editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6610-6630 id: tanaka26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6610 lastpage: 6630 published: 2026-08-06 00:00:00 +0000 - title: 'Particle Dynamics for Latent-Variable Energy-Based Models' abstract: 'Latent-variable energy-based models (LV-EBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood training as a saddle problem over distributions on the latent and joint manifolds and view the inner updates as coupled {Wasserstein} gradient flows. The resulting algorithm alternates overdamped Langevin updates for a joint negative pool and for conditional latent particles with stochastic parameter ascent, requiring no discriminator or auxiliary networks. We prove existence and convergence under standard smoothness and dissipativity assumptions, with decay rates in KL divergence and {Wasserstein}-2 distance. The saddle-point view further yields an {ELBO} strictly tighter than bounds obtained with restricted amortized posteriors. Our method is evaluated on numerical approximations of physical systems and performs competitively against comparable approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/tang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/tang26a/tang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-tang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shiqin family: Tang - given: Shuxin family: Zhuang - given: Runsheng family: Yu - given: Rong family: Feng - given: Shujian family: Yu - given: Hongzong family: Li - given: Mingyang family: Zhao - given: Gaofeng family: Meng editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6631-6644 id: tang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6631 lastpage: 6644 published: 2026-08-06 00:00:00 +0000 - title: 'Robust and Computationally Efficient Linear Contextual Bandits under Adversarial Corruption and Heavy-Tailed Noise' abstract: 'We study linear contextual bandits under adversarial corruption and heavy-tailed noise with finite $(1+\epsilon)$-th moments for some $\epsilon \in (0,1]$. Existing work that addresses both adversarial corruption and heavy-tailed noise relies on a finite variance assumption and suffers from computational inefficiency. We propose the first computationally efficient algorithm based on online mirror descent that is robust to both adversarial corruption and heavy-tailed noise. While the existing algorithm incurs $\mathcal{O}(t\log T)$ computational cost per round, our algorithm reduces this to $\mathcal{O}(1)$ per round. We establish an additive regret bound consisting of a term depending on the $(1+\epsilon)$-moment bound of the noise and a term depending on the total amount of corruption. This bound unifies and extends previous guarantees for (generalized) linear contextual bandits under adversarial corruption and heavy-tailed noise. In particular, when $\epsilon = 1$, it recovers existing guarantees under finite-variance assumptions. When no corruption is present, it achieves the same regret rate as existing results for linear contextual bandits with heavy-tailed noise in the general setting. Moreover, the algorithm requires only upper bounds on the noise moment and the total amount of corruption, while still guaranteeing sublinear regret.' volume: 337 URL: https://proceedings.mlr.press/v337/tani26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/tani26a/tani26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-tani26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Naoto family: Tani - given: Futoshi family: Futami editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6645-6676 id: tani26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6645 lastpage: 6676 published: 2026-08-06 00:00:00 +0000 - title: 'Positive-Unlabeled Regression: learning from partially labeled quantitative outcomes' abstract: 'We study a novel machine learning problem: Positive-Unlabeled Regression (PUR), which extends the classical Positive-Unlabeled ({PU}) learning framework to regression setting with a non-negative, discrete target variable. This setting arises naturally in applications where only some positive quantitative outcomes are reported, while the absence of a label may either indicate a true zero outcome or an unreported positive value. Applications include predicting the number of diseases a patient may have, the number of complications following an illness, or the advancement stage of a disease. We formalize the PUR problem and highlight the limitations of naive approaches that either use reported target variable or discard unlabeled data. To account for the inherent bias in such strategies, we propose two principled methods. The first is based on calibration of regression estimates using posterior probabilities from classical {PU} learning. The second builds on an empirical risk minimization framework, restating the target risk as a weighted function dependent on the instance-specific propensity score. We demonstrate both theoretically and empirically that the proposed approaches yield improved performance over standard baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/teisseyre26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/teisseyre26a/teisseyre26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-teisseyre26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Paweł family: Teisseyre - given: Jan family: Mielniczuk editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6677-6700 id: teisseyre26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6677 lastpage: 6700 published: 2026-08-06 00:00:00 +0000 - title: 'EVIA: Entropic Variational Inference Auto-encoding' abstract: 'We present Entropic Variational Inference Auto-encoding ({EVIA}), a novel framework that extends classical variational approaches—including WAEs and {AAEs}, by incorporating entropy regularization. This regularization yields an entropic objective characterized by a closed-form {Gibbs} posterior, established via the {Donsker}–{Varadhan} representation. Consequently, this formulation facilitates efficient sampling strategy, allowing the model to perform high-fidelity autoencoding while jointly ensuring accurate distributional alignment. Empirical results demonstrate {EVIA}’s strong, consistent performance across diverse generative modeling tasks, including posterior estimation, variational inference, and image inpainting.' volume: 337 URL: https://proceedings.mlr.press/v337/teng26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/teng26a/teng26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-teng26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yunfei family: Teng - given: Zhichao family: Chen - given: Xinyu family: Chen - given: Lulu family: Tang - given: Sixin family: Zhang - given: Zhouchen family: Lin editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6701-6717 id: teng26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6701 lastpage: 6717 published: 2026-08-06 00:00:00 +0000 - title: 'On Pairwise Quantile Regression - Statistical Guarantees and Applications' abstract: 'Quantile regression provides a powerful tool for summarizing the conditional distribution of a real-valued random variable (r.v.) of interest $Y$ as a function of covariates $Z$ in cases where it shows a large dispersion with high probability, going beyond the situation where standard least square regression is informative/predictive. This article aims to extend this methodology to the pairwise setting, where the variable to be explained is a similarity score between two independent observations (e.g., pixelated ID photos used as input to biometric systems), and the explanatory variables consist of the pair of covariates attached to these observations, such as age or hair color. We establish theoretical guarantees for solutions of this statistical learning problem, considered here as empirical minimizers of a pairwise version of the pinball loss. Leveraging sharp concentration results for $U$-processes, we prove generalization bounds and identify mild conditions under which fast learning rates can be achieved. Confirming the probabilistic analysis, experiments based on simulation data also provide solid empirical evidence of the validity of the methodology promoted here for pairwise quantile regression. Finally, its usefulness from an application perspective is demonstrated by a detailed study aimed at analyzing errors in similarity scoring for facial recognition.' volume: 337 URL: https://proceedings.mlr.press/v337/therezien26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/therezien26a/therezien26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-therezien26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Romain family: Therezien - given: Stephan family: Clémençon - given: Fantin family: Girard - given: Hamza family: El-Abdouni editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6718-6739 id: therezien26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6718 lastpage: 6739 published: 2026-08-06 00:00:00 +0000 - title: 'Benign Overfitting with Quantum Kernels' abstract: 'Kernel methods compare inputs through feature maps. Quantum kernels follow the same principle: input data are encoded into quantum states, which define quantum feature representations in {Hilbert} spaces. Kernel values are then obtained by estimating inner products between these states using suitable quantum circuit measurements. As a result, quantum kernels may be intractable to compute classically while remaining efficiently computable on quantum hardware, potentially leading to a quantum advantage. However, designing effective quantum kernels remains a major challenge. Many quantum kernels, such as the fidelity kernel, suffer from exponential concentration. This results in near-identity kernel matrices that fail to capture meaningful data correlations and lead to overfitting and poor generalization. In this paper, we propose a novel strategy for constructing quantum kernels that achieve good generalization performance, drawing inspiration from benign overfitting in classical machine learning. We introduce the concept of Local-Global quantum kernels, which combine two components: a local quantum kernel based on measurements of small subsystems, and a global quantum kernel derived from full-system measurements. To support the effectiveness of the proposed construction, we show theoretically and empirically that Local-Global quantum kernels exhibit benign overfitting.' volume: 337 URL: https://proceedings.mlr.press/v337/tomasi26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/tomasi26a/tomasi26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-tomasi26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Joachim family: Tomasi - given: Sandrine family: Anthoine - given: Hachem family: Kadri editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6740-6766 id: tomasi26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6740 lastpage: 6766 published: 2026-08-06 00:00:00 +0000 - title: 'Not Just How Much, But Where: Decomposing Epistemic Uncertainty into Per-Class Contributions' abstract: 'In safety-critical classification, the cost of failure is often asymmetric. Yet {Bayesian} deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), which cannot distinguish whether a model’s ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector $\mathcal{C}_k(x)=\sigma_k^{2}/(2\mu_k)$, with $\mu_k = \mathbb{E}[p_k]$ and $\sigma_k^2 = \mathrm{Var}[p_k]$ across posterior samples. The decomposition follows from a second-order {Taylor} expansion of the entropy; the $1/\mu_k$ weighting corrects boundary suppression and makes $\mathcal{C}_k$ comparable across rare and common classes. By construction $\sum_k \mathcal{C}_k \approx \mathrm{MI}$, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of $\mathcal{C}_k$, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class $\mathcal{C}_k$ reduces selective risk by 34.7% over MI and 56.2% over variance baselines; (ii) out-of-distribution detection on clinical and image benchmarks, where $\sum_k \mathcal{C}_k$ achieves the highest AUROC and the per-class view exposes asymmetric shifts invisible to MI; and (iii) a controlled label-noise study in which $\sum_k \mathcal{C}_k$ shows less sensitivity to injected aleatoric noise than MI under end-to-end {Bayesian} training, while both metrics degrade under transfer learning. Across all tasks, the quality of the posterior approximation shapes uncertainty at least as strongly as the choice of metric, suggesting that how uncertainty is propagated through the network matters as much as how it is measured.' volume: 337 URL: https://proceedings.mlr.press/v337/toure26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/toure26a/toure26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-toure26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Mame Diarra family: Toure - given: David A. family: Stephens editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6767-6806 id: toure26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6767 lastpage: 6806 published: 2026-08-06 00:00:00 +0000 - title: 'Improving TabPFN’s Synthetic Data Generation by Integrating Causal Structure' abstract: 'Synthetic tabular data generation addresses data scarcity and privacy constraints in a variety of domains. Tabular Prior-Data Fitted Network ({TabPFN}), a recent foundation model for tabular data, has been shown capable of generating high-quality synthetic tabular data. However, {TabPFN} is autoregressive: features are generated sequentially by conditioning on the previous ones, depending on the order in which they appear in the input data. We demonstrate that when the feature order conflicts with causal structure, the model produces spurious correlations that impair its ability to generate synthetic data and preserve causal effects. We address this limitation by integrating causal structure into {TabPFN}’s generation process through two complementary approaches: Directed Acyclic Graph ({DAG})-aware conditioning, which samples each variable given its causal parents, and a partially directed acyclic graph (PDAG)-based strategy for scenarios with partial causal knowledge. We evaluate these approaches on controlled benchmarks and six CSuite datasets, assessing structural fidelity, distributional quality, and Average Treatment Effect ({ATE}) preservation. Across most settings, {DAG}-aware conditioning improves the quality and stability of synthetic data relative to vanilla {TabPFN}. Under partial causal knowledge, the oracle partially directed acyclic graph (oracle-PDAG), which orients only the edges into the colliders, shows moderate gains, while the benefit of a Completed Partially Directed Acyclic Graph (CPDAG) discovered from data depends on how well the causal structure is recovered. These results indicate that reliable causal structure, even partial, can be injected into {TabPFN} at inference time, without parameter updates, to improve synthetic data quality.' volume: 337 URL: https://proceedings.mlr.press/v337/tugnoli26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/tugnoli26a/tugnoli26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-tugnoli26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Davide family: Tugnoli - given: Andrea family: De Lorenzo - given: Marco family: Virgolin - given: Giovanni family: Cinà editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6807-6850 id: tugnoli26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6807 lastpage: 6850 published: 2026-08-06 00:00:00 +0000 - title: 'Online Learning for Project Selection in Hedonic Project Games' abstract: 'We study Hedonic Project Games, a model in which agents select projects with divisible rewards while holding subjective preferences over coalition composition. This framework addresses a key gap in existing models: agents simultaneously care about who they collaborate with and what they work on. We extend this framework to an online learning setting in which rewards and preferences are initially unknown and learned through repeated interactions. We develop a decentralized variance-reduced stochastic policy-gradient method that provably converges to approximate {Nash} equilibria using single-sample gradient estimates, and an unbiased momentum variant that achieves faster convergence at the cost of additional curvature computation. We provide sample-complexity guarantees for both methods and show that exploiting the game’s additive pairwise structure reduces the interactions required to reach an approximate equilibrium by a polynomial factor in the number of agents. Experiments on synthetic instances and a real-world crowdsourcing dataset validate the theoretical convergence rates and demonstrate the advantages of momentum-based variance reduction over momentum-free baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/valizadeh26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/valizadeh26a/valizadeh26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-valizadeh26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jaber family: Valizadeh - given: Dongmo family: Zhang - given: Omar family: Mubin - given: Ray family: Telikani editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6851-6861 id: valizadeh26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6851 lastpage: 6861 published: 2026-08-06 00:00:00 +0000 - title: 'A Causal Markov Condition for Value' abstract: 'This paper proposes a causal independence principle for *value*—the *value Causal {Markov} Condition* (v-CMC)—and develops the conceptual and mathematical foundations of a "causal value theory" linking causality and utility. After motivating a local formulation of the v-CMC, we introduce a probability–value duality that translates standard causal-inference results into the value setting. In particular, we formulate local, global, and decomposition versions of the v-CMC and prove their equivalence. We also define $v$-separation and show that it is sound and complete for conditional value independence. Furthermore, we derive a {Bellman}-type recursion as a special case of the v-CMC, thereby generalizing standard {Bellman} recursion from linear chains to causal DAGs. Finally, we show how the v-CMC supports modular transfer and updating of utility information across causal contexts and develop algorithms for causally structured utility elicitation and canonical influence-diagram construction.' volume: 337 URL: https://proceedings.mlr.press/v337/vassend26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/vassend26a/vassend26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-vassend26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Olav Benjamin family: Vassend editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6862-6884 id: vassend26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6862 lastpage: 6884 published: 2026-08-06 00:00:00 +0000 - title: 'Fisher8: Stabilizing Neural Heteroscedastic Regression via Output-Layer Fisher Geometry' abstract: 'Training neural networks to jointly predict mean and uncertainty estimates from noisy observations can be unstable, prompting a series of independent stabilization efforts. We argue that these interventions highlight a common underlying issue where gradient steps are poorly aligned with the geometry of the loss landscape. To better align updates with local curvature, we derive Fisher8, an output-layer gradient correction that reorients and rescales updates using {Fisher} geometry rather than {Euclidean} geometry. Unlike past stabilizers, Fisher8 introduces no data-dependent hyperparameters beyond learning rate and admits an approximate KL trust radius between successive predictive distributions. We show that prior stabilizers converge on overlapping components of this geometric correction. Across multidimensional regression and representation-learning tasks, Fisher8 obtains superior likelihood–error tradeoffs, predicts calibrated uncertainty estimates, and learns rich uncertainty-aware feature spaces.' volume: 337 URL: https://proceedings.mlr.press/v337/vemuganti26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/vemuganti26a/vemuganti26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-vemuganti26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Sumedh family: Vemuganti - given: Nickvash family: Kani editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6885-6899 id: vemuganti26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6885 lastpage: 6899 published: 2026-08-06 00:00:00 +0000 - title: 'APIC: Amortized Physics-Informed Calibration using Neural Processes' abstract: 'Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy–O’Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, per-instance formulation limits scalability across families of related systems. We introduce Amortized Physics-Informed Calibration ({APIC}), a population-level extension of KOH that leverages Neural Processes to perform scalable {Bayesian} inference across realizations. Our framework employs a two-branch latent architecture to disentangle instance-specific physical parameters from shared, state-dependent structural discrepancies. By integrating differentiable physics into an amortized inference backbone, {APIC} enables rapid calibration of unseen realizations from sparse observations while quantifying uncertainty. Experiments on the damped spring oscillator, the Lotka–Volterra system, and the advection–diffusion {PDE} with misspecified physics demonstrate improved parameter recovery and consistent identification of the systemic discrepancy structure compared to other calibration approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/venkataramanan26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/venkataramanan26a/venkataramanan26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-venkataramanan26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Aishwarya family: Venkataramanan - given: Sai Karthikeya family: Vemuri - given: Joachim family: Denzler editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6900-6916 id: venkataramanan26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6900 lastpage: 6916 published: 2026-08-06 00:00:00 +0000 - title: 'Structured Credal Learning' abstract: 'Real-world learning tasks often encounter uncertainty due to covariate shift and noisy or inconsistent labels. However, existing robust learning methods merge these effects into a single distributional uncertainty set. In this work, we introduce a novel structured credal learning framework that explicitly separates these two sources. Specifically, we derive geometric bounds on the total variation diameter of structured credal sets and demonstrate how this quantity decomposes into contributions from covariate shift and expected label disagreement. This decomposition reveals a *gating effect*: covariate modulates how much label disagreement contributes to the joint uncertainty such that seemingly benign covariate shifts can substantially increase the effective uncertainty. We also establish finite-sample concentration bounds in a fixed covariate regime and demonstrate that this quantity can be efficiently estimated. Lastly, we show that robust optimization over these structured credal sets reduces to a tractable discrete min–max problem, avoiding ad-hoc robustness parameters. Overall, our approach provides a principled and practical foundation for robust learning under combined covariate and label mechanism ambiguity.' volume: 337 URL: https://proceedings.mlr.press/v337/venkatesh26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/venkatesh26a/venkatesh26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-venkatesh26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Varun family: Venkatesh - given: Eyke family: Hüllermeier - given: Bernd family: Bischl - given: Mina family: Rezaei editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6917-6952 id: venkatesh26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6917 lastpage: 6952 published: 2026-08-06 00:00:00 +0000 - title: 'Markovian Compression: Looking to the Past Helps Accelerate the Future' abstract: 'This paper deals with distributed optimization problems that use compressed communication to achieve efficient performance and mitigate communication bottleneck. We propose a family of compression schemes in which operators transform vectors fed to their input according to a {Markov} chain, i.e. the stochasticity of the compressors depends on previous iterations. The compressors are implemented in the vanilla Quantized Stochastic Gradient Descent (QSGD) algorithm, and, to further improve the efficiency and convergence rate, in the momentum accelerated QSGD. We provide convergence results for our algorithms with Markovian compressors, the analysis covers non-convex, {Polyak-Lojasiewicz}, and strongly convex cases. To demonstrate the applicability of our approach to distributed data-parallel optimization problems, we conduct experiments on the {CIFAR-10} and GLUE datasets with the Resnet-18 and DeBERTaV3 models. Practical results show the superiority of methods that use our compressor design over existing schemes.' volume: 337 URL: https://proceedings.mlr.press/v337/veprikov26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/veprikov26a/veprikov26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-veprikov26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Andrey family: Veprikov - given: Vladimir family: Solodkin - given: Mikhail family: Rudakov - given: Petr family: Babkin - given: Aleksandr family: Beznosikov editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6953-6998 id: veprikov26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6953 lastpage: 6998 published: 2026-08-06 00:00:00 +0000 - title: 'Collapse-Aware Regularization for Reliable Reasoning Under Distribution Shift' abstract: 'Reliable reasoning requires models to generalize under distribution shifts, yet in-distribution validation loss often fails to identify checkpoints that remain reliable out of distribution. We study representation collapse in Transformer hidden states as an internal degeneration that may reduce the effective capacity needed for multi-step inference. We characterize two complementary collapse signals: spectral capacity collapse, measured by the effective rank of layerwise representation covariance, and geometric alignment collapse, measured by average cosine alignment. We then propose the Collapse Risk Criterion (CRC), an ID-computable diagnostic score estimated from in-distribution validation representations. CRC is not a formal {OOD} guarantee, but a practical surrogate for {OOD}-free checkpoint selection. Across four reasoning benchmarks and three Transformer backbones, CRC correlates more strongly with {OOD} reasoning error than ID validation loss and standard confidence-based reliability scores. CRC-aware checkpoint selection improves {OOD} performance under depth/difficulty and template/rule shifts with minimal ID degradation. As an extension, collapse-aware training with a CRC-based regularizer improves average {OOD} performance in all evaluated dataset–backbone settings. Our results suggest that monitoring representation collapse is a simple and useful tool for improving reasoning reliability without {OOD} validation data.' volume: 337 URL: https://proceedings.mlr.press/v337/vo26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/vo26a/vo26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-vo26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Quynh family: Vo - given: Cong-Duy T family: Nguyen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 6999-7022 id: vo26a issued: date-parts: - 2026 - 8 - 6 firstpage: 6999 lastpage: 7022 published: 2026-08-06 00:00:00 +0000 - title: 'Upper entropy for 2-monotone lower probabilities' abstract: 'Uncertainty quantification is a key aspect in many tasks such as model selection/regularization, or quantifying prediction uncertainties to perform active learning or {OOD} detection. Within credal approaches that consider modeling uncertainty as probability sets, upper entropy plays a central role as an uncertainty measure. This paper is devoted to the computational aspect of upper entropies, providing an exhaustive algorithmic and complexity analysis of the problem. In particular, we show that the problem has a strongly polynomial solution, and propose many significant improvements over past algorithms proposed for 2-monotone lower probabilities and their specific cases.' volume: 337 URL: https://proceedings.mlr.press/v337/vu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/vu26a/vu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-vu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tuan-Anh family: Vu - given: Sebastien family: Destercke - given: Frédéric family: Pichon editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7023-7035 id: vu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7023 lastpage: 7035 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Informative Attention Weights for Person Re-Identification' abstract: 'Attention mechanisms are widely used in deep learning and have been incorporated into DNNs for person Re-Identification (Re-ID) to enhance discriminative feature learning. Existing attention modules, including self-attention and channel attention, learn attention weights that quantify the importance of feature tokens or feature channels. However, existing attention methods do not explicitly ensure that the attention weights are informative for predicting the identity of the person in the input image, and may consequently introduce noisy information from the input image. To address this issue, we propose a novel method termed Reduction of Information Bottleneck loss (RIB), motivated by the principle of the Information Bottleneck (IB). A novel distribution-free and efficient variational upper bound for the IB loss (IBB), which can be optimized by standard {SGD}, is derived and incorporated into the training loss of the RIB models. RIB is applied to DNNs with self-attention through a novel Differentiable Channel Selection Attention module (DCS-Attention), which selects informative channels to compute attention weights, leading to RIB-DCS. It is also integrated with existing channel attention modules to learn informative channel weights, leading to RIB-CA. Both RIB-DCS and RIB-CA are applied to fixed backbones and learnable backbones with Differentiable Neural Architecture Search (DNAS). Extensive experiments on multiple person Re-ID benchmarks show that RIB significantly improves prediction accuracy, including in occluded person Re-ID, by learning more discriminative and identity-informative features. The code of our work is available at https://github.com/Statistical-Deep-Learning/RIB-ReID.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26b/wang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yancheng family: Wang - given: Nebojsa family: Jojic - given: Yingzhen family: Yang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7036-7071 id: wang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 7036 lastpage: 7071 published: 2026-08-06 00:00:00 +0000 - title: 'Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Study' abstract: 'Epistemic uncertainty in neural networks is commonly modeled using two second-order paradigms: distribution-based representations, which rely on posterior parameter distributions, and set-based representations based on credal sets (convex sets of probability distributions). These frameworks are often regarded as fundamentally non-comparable due to differing semantics, assumptions, and evaluation practices, leaving their relative merits unclear. Empirical comparisons are further confounded by variations in the underlying predictive models. To clarify this issue, we present a controlled comparative study enabling principled, like-for-like evaluation of the two paradigms. Both representations are constructed from the same finite collection of predictive distributions generated by a shared neural network, isolating representational effects from predictive accuracy. Our study evaluates each representation through the lens of 3 uncertainty measures across 8 benchmarks, including selective prediction and out-of-distribution detection, spanning 6 underlying predictive models and 10 independent runs per configuration. Our results show that meaningful comparison between these seemingly non-comparable frameworks is both feasible and informative, providing insights into how second-order representation choices impact practical uncertainty-aware performance.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26c/wang26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Kaizheng family: Wang - given: Yunjia family: Wang - given: Fabio family: Cuzzolin - given: David family: Moens - given: Hans family: Hallez - given: Siu Lun family: Chau editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7072-7102 id: wang26c issued: date-parts: - 2026 - 8 - 6 firstpage: 7072 lastpage: 7102 published: 2026-08-06 00:00:00 +0000 - title: 'Recursive Fréchet Mean Estimation' abstract: 'Estimating the mean of manifold-valued data is a central problem in modern statistics, yet it remains challenging due to the lack of a closed-form expression for the {Fréchet} mean. The gradient descent algorithm is widely used to approximate this quantity across various applications. Although generally effective, it can be computationally intensive for large datasets, as each iteration requires evaluating gradients with respect to the entire dataset. To address these limitations, we propose a tree-based, Recursive {Fréchet} Mean Estimator ({RFME}), tailored to data on manifolds. The proposed method leverages a hierarchical aggregation strategy to reduce computational complexity while preserving statistical accuracy. We establish the weak consistency of {RFME} with respect to the population {Fréchet} mean and discuss its computational properties. Through simulation studies and real-world applications, we demonstrate that {RFME} achieves competitive estimation accuracy with substantially improved efficiency. Moreover, as a generalization of the incremental {Fréchet} mean estimator, {RFME} also offers enhanced flexibility while maintaining practical advantages.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26d/wang26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Cheng family: Wang - given: Carlos J family: Soto editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7103-7120 id: wang26d issued: date-parts: - 2026 - 8 - 6 firstpage: 7103 lastpage: 7120 published: 2026-08-06 00:00:00 +0000 - title: 'From Moves to Paths: A Hierarchical Framework for Trajectory Representation Learning' abstract: 'Trajectory representation learning (TRL) seeks to convert trajectory data into low-dimensional embeddings for various downstream tasks. Existing methods are limited to a single perspective: GPS-based approaches capture dynamic details but lack semantic context, while route-based methods preserve structure but lose fine-grained motion patterns. To address these limitations, we propose a trajectory representation model with multi-perspective fusion, MPH, where \underline{M} denotes the Motion modality (GPS), \underline{P} denotes the planned path modality (Route), and\underline{H} signifies the Hierarchical encoding and fusion strategy. MPH first map-matches raw GPS trajectories to route sequences and designs dedicated encoders to extract dynamic behavioral patterns and static semantic features respectively. Based on this, MPH leverages a cross-attention mechanism for modality interaction and fusion, producing fused route representations that are hierarchically aggregated into trajectory-level embeddings. Furthermore, we introduce two self-supervised tasks to train the model. Contrastive learning is employed to align road segment representations across the two perspectives, while the dual-mask prediction task strengthens contextual modeling by jointly reconstructing masked road segment identities and their corresponding temporal information. Experiments on two real-world datasets show that MPH outperforms all baselines across different tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26e/wang26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Chundong family: Wang - given: Xiangtian family: Zheng - given: Qingbo family: Hao - given: Yongxin family: Zhao - given: Yixuan family: Song - given: Jia family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7121-7136 id: wang26e issued: date-parts: - 2026 - 8 - 6 firstpage: 7121 lastpage: 7136 published: 2026-08-06 00:00:00 +0000 - title: 'On the Effect of Sampling Diversity in Scaling LLM Inference' abstract: 'Large language model ({LLM}) scaling inference is key to unlocking greater performance, and leveraging diversity has proven an effective way to enhance it. Motivated by the observed relationship between solution accuracy and meaningful response diversity, we systematically study the effect of prompt diversity in scaling inference. We theoretically explain why diversified sampling improves Best-of-N scaling, showing that responses generated from diverse prompts after Best-of-N selection exhibit significantly lower error rates than those produced from stationary prompts. Building on this analysis, we derive a diversity-fidelity trade-off principle, that guides the design of sampling strategies introducing diversity. From this guidance, we instantiate a family of effective perturbation styles. We theoretically and empirically characterize when diversified exploration remains effective, demonstrating that it works under a variety of conditions, and we further show that under majority voting, diversity may vanish. We systematically evaluate the effectiveness of sampling diversity and show that, when applied appropriately in different contexts, meaningful perturbations yield stronger, task-dependent gains as diversity increases. Overall, this work provides a systematic analysis that offers a theoretical and empirical foundation for understanding the effect of diversity in {LLM} inference-time scaling.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26f/wang26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tianchun family: Wang - given: Yuanzhou family: Chen - given: Zichuan family: Liu - given: Jonathan family: Light - given: Weiyang family: Liu - given: Haifeng family: Chen - given: Xiang family: Zhang - given: Wei family: Cheng editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7137-7167 id: wang26f issued: date-parts: - 2026 - 8 - 6 firstpage: 7137 lastpage: 7167 published: 2026-08-06 00:00:00 +0000 - title: 'Bandit Learning for Online Scheduling with Immediate Decision' abstract: 'Motivated by latency-critical streaming domains such as IoT data processing and cloud resource allocation, we investigate the problem of Online Scheduling with Immediate Decision, where a scheduler must instantly decide whether to accept an incoming task without buffering. We consider a system with $M$ identical machines handling tasks with fixed processing lengths and stochastic, initially unknown rewards. A distinct feature of our model is preemption with abandonment: while a machine can interrupt a running task to accept a more valuable new arrival, the preempted task is permanently discarded, yielding no reward and no feedback, which is crucial for learning. We first analyze the setting with known rewards, deriving a worst-case competitive ratio lower bound and proposing the near-optimal Maximum Remaining Density First (MRDF) algorithm. For the challenging case of unknown rewards with censored feedback, we design an efficient bandit algorithm, Scheduling Upper Confidence Bound (S-{UCB}), which balances exploration and exploitation to achieve an $O(\log T)$ regret over time horizon $T$. Experimental results demonstrate the efficacy of the proposed algorithms against standard baselines.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26g.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26g/wang26g.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26g.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zilong family: Wang - given: Yuhao family: Zhang - given: Zhewei family: Wei - given: Shuai family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7168-7199 id: wang26g issued: date-parts: - 2026 - 8 - 6 firstpage: 7168 lastpage: 7199 published: 2026-08-06 00:00:00 +0000 - title: 'Graph Contrastive Learning with Low-Rank Regularization and Low-Rank Attention for Noisy Node Classification' abstract: 'Graph Neural Networks (GNNs) have shown strong performance in learning node representations and node classification, but their effectiveness can be substantially degraded by noise in real-world graph data. To address this challenge, we introduce a robust and innovative node representation learning method named Graph Contrastive Learning with Low-Rank Regularization, or GCL-LRR, which follows a two-stage transductive learning framework for node classification. In the first stage, the GCL-LRR encoder is trained via prototypical contrastive learning with a low-rank regularization objective, and in the second stage, the learned representations are used by a linear transductive classifier to predict labels for unlabeled nodes. Our GCL-LRR is inspired by the Low Frequency Property (LFP) of the graph data and its labels, and it is also theoretically motivated by our sharp generalization bound for transductive learning. Our theoretical result is among the first to theoretically demonstrate the advantage of low-rank regularization in transductive learning, which is also supported by strong empirical results. To further enhance the performance of GCL-LRR, we present an improved model named GCL-LR-Attention, which incorporates a novel LR-Attention layer into GCL-LRR. GCL-LR-Attention reduces the kernel complexity of GCL-LRR and contributes to a tighter generalization bound, leading to improved performance. Extensive evaluations on standard benchmark datasets evidence the effectiveness and robustness of both GCL-LRR and GCL-LR-Attention. The code of GCL-LRR and GCL-LR-Attention is available at https://github.com/Statistical-Deep-Learning/GCL-LR-Attention.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26h.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26h/wang26h.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26h.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yancheng family: Wang - given: Ping family: Li - given: Yingzhen family: Yang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7200-7228 id: wang26h issued: date-parts: - 2026 - 8 - 6 firstpage: 7200 lastpage: 7228 published: 2026-08-06 00:00:00 +0000 - title: 'Stationary Robust Mean-Field Games under Model Mismatches' abstract: 'Deploying multi-agent reinforcement learning ({MARL}) in the real world is often limited by model mismatches between the training simulators and the true environment, which could be further amplified through strategic interactions and result in severe performance degradation upon deployment. Distributional robustness offers a principled response by optimizing policies against worst-case transition models drawn from an uncertainty set, but standard robust {MARL} frameworks become increasingly intractable as the number of agents grows. This paper develops an infinite-horizon, stationary mean-field game framework that incorporates distributional model uncertainty directly into the population-coupled dynamics. We establish a robust dynamic programming principle with a contractive {Bellman} operator and prove the existence of a stationary robust mean-field equilibrium via a fixed-point argument. We further develop the first concrete algorithm with convergence guarantees. We then connect the mean-field solution to a finite-population robust game whose ambiguity sets depend on the empirical distribution, showing that the mean-field equilibrium policy induces approximate equilibrium behavior as the population size increases. Under a contractive robust-dynamics regime, we further obtain explicit non-asymptotic error bounds. Numerical experiments further illustrate the qualitative and quantitative impact of robustness under multiple uncertainty models, validating our theoretical findings.' volume: 337 URL: https://proceedings.mlr.press/v337/wang26i.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wang26i/wang26i.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wang26i.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yue family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7229-7272 id: wang26i issued: date-parts: - 2026 - 8 - 6 firstpage: 7229 lastpage: 7272 published: 2026-08-06 00:00:00 +0000 - title: 'Hierarchical Bayesian Quadrature' abstract: 'Numerical integration is a cornerstone of various scientific computing applications, such as engineering simulations and model evidence computations in probabilistic machine learning. {Bayesian} Quadrature uses {Gaussian} process surrogates that explicitly encode structural assumptions about the integrand to obtain integral estimates with quantified uncertainty. These surrogates are predominantly based on stationary covariance functions, which results in model misspecification for integrands exhibiting nonstationary behavior. We tackle this issue through an adaptively growing, tree-based partition of the integration domain into local stationary models. Our method recombines the local integral estimates through a hierarchy of GP conditioning that reintroduces cross-subdomain correlations, while model selection criteria control the tree growth to avoid unnecessary partitioning. The resulting algorithm is simple, requires no {MCMC}, and adapts its evaluation budget to local integrand complexity. On benchmark integration problems and a model evidence computation for an epidemiological model, Hierarchical {Bayesian} Quadrature achieves substantial gains over standard {Bayesian} Quadrature on nonstationary integrands while matching its performance on stationary ones.' volume: 337 URL: https://proceedings.mlr.press/v337/weiland26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/weiland26a/weiland26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-weiland26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Tim family: Weiland - given: Toni family: Karvonen - given: Philipp family: Hennig editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7273-7289 id: weiland26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7273 lastpage: 7289 published: 2026-08-06 00:00:00 +0000 - title: 'Efficient Federated Conformal Prediction with Group-Conditional Guarantee' abstract: 'Deploying trustworthy {AI} systems requires principled uncertainty quantification. Conformal prediction ({CP}) is a widely used framework for constructing prediction sets with distribution-free coverage guarantees. In many practical settings, including healthcare, finance, and mobile sensing, the calibration data required for {CP} are distributed across multiple clients, each with its own local data distribution. In this federated setting, data can often be partitioned into, potentially overlapping, groups, which may reflect client-specific strata or cross-cutting attributes such as demographic or semantic categories. We propose \emph{group-conditional} federated conformal prediction (GC-FCP), a federated extension of conditional conformal calibration for a target mixture over prespecified groups. GC-FCP constructs mergeable, atom-stratified coresets from local calibration scores, enabling compact aggregation at the server when the number of active atoms is moderate. Experiments on synthetic and real-world datasets validate the performance of GC-FCP compared to centralized calibration baselines. The code of our work can be found at https://github.com/HaifengWen/GC-FCP.' volume: 337 URL: https://proceedings.mlr.press/v337/wen26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wen26a/wen26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wen26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Haifeng family: Wen - given: Osvaldo family: Simeone - given: Hong family: Xing editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7290-7313 id: wen26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7290 lastpage: 7313 published: 2026-08-06 00:00:00 +0000 - title: 'Weighted Sequential Bayesian Inference for Non-Stationary Linear Contextual Bandits' abstract: 'In non-stationary linear contextual bandits, existing efficient algorithms typically rely on the Weighted Regularized Least-Squares (WRLS) estimator. Because WRLS only provides point estimates, previous methods typically construct surrogate distributions when aiming to perform {Bayesian}-like randomized exploration. To more properly establish the {Bayesian} principles, we introduce *Weighted Sequential {Bayesian}* (WSB) inference, which forms a sequence of posteriors over a sequence of non-stationary reward parameters. This {Bayesian} take allows us to isolate the influence of initial beliefs into a dynamic prior penalty evaluated through the posterior covariance, which typically decreases over time. Building on this framework, we instantiate three WSB-based algorithms for exploration: *WSB-LinUCB*, *WSB-RandLinUCB*, and *WSB-LinTS*. By extending a refined drift analysis to randomized exploration without requiring local norms, we establish frequentist regret guarantees that match state-of-the-art WRLS-based baselines. Empirically, WSB’s dynamic prior penalty reduces over-conservatism, allowing our algorithms to consistently match or exceed their WRLS-based counterparts. Lastly, we also provide a simplified proof for the time-uniform concentration of vector-valued martingales, a critical subroutine used throughout the literature, that might be of independent interest.' volume: 337 URL: https://proceedings.mlr.press/v337/werge26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/werge26a/werge26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-werge26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Nicklas family: Werge - given: Yi-Shan family: Wu - given: Abdullah family: Akgül - given: Melih family: Kandemir editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7314-7340 id: werge26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7314 lastpage: 7340 published: 2026-08-06 00:00:00 +0000 - title: 'Single-Network Asymptotics for Causal Inference with Partial Network Data' abstract: 'Randomized experiments are a staple in academic research, policy, and industry. Interference, when the outcome of one unit depends on the treatment status of other units, can cause bias in estimates of the treatment effect. Statistical corrections rely on knowing the underlying network of transmission pathways. Often, though, it is only possible to partially observe the network (e.g., through node subsamples, egocentric designs, respondent-driven sampling, or aggregated relational data). We develop a single-network asymptotic framework for inference about treatment effects in this regime. Starting from a structural causal model and exposure mapping, we assume a flexible class of generative network models consistent with the partial measurements and construct feasible proxy exposures by averaging over plausible completions of the network. We then study moment-based estimators for response parameters and treatment effects under dependence, and give conditions for consistency and asymptotic normality together with an explicit rate requirement ensuring that network-estimation error is first-order negligible. Simulations and an empirical replication illustrate how the theory maps to finite-sample workflows for interference with partial network data.' volume: 337 URL: https://proceedings.mlr.press/v337/wilkins-reeves26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wilkins-reeves26a/wilkins-reeves26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wilkins-reeves26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Steven family: Wilkins-Reeves - given: Shane family: Lubold - given: Arun family: Chandrasekhar - given: Tyler family: McCormick editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7341-7369 id: wilkins-reeves26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7341 lastpage: 7369 published: 2026-08-06 00:00:00 +0000 - title: 'Simplex-to-Euclidean Bijection for Conjugate and Calibrated Multiclass Gaussian Process Classification' abstract: 'We propose a conjugate and calibrated {Gaussian} process (GP) model for multi-class classification by exploiting the geometry of the probability simplex. Our approach uses Aitchison geometry to map simplex-valued class probabilities to an unconstrained {Euclidean} representation, turning classification into a GP regression problem with fewer latent dimensions than standard multi-class GP classifiers. This yields conjugate inference and reliable predictive probabilities without relying on distributional approximations in the model construction. The method is compatible with standard sparse GP regression techniques, enabling scalable inference on larger datasets. Empirical results show well-calibrated and competitive performance across synthetic and real-world datasets.' volume: 337 URL: https://proceedings.mlr.press/v337/williams26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/williams26a/williams26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-williams26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Bernardo family: Williams - given: Harsha Vardhan family: Tetali - given: Arto family: Klami - given: Marcelo family: Hartmann editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7370-7386 id: williams26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7370 lastpage: 7386 published: 2026-08-06 00:00:00 +0000 - title: 'Building a Bridge Between the Shapley Value, Prime Implicants and Counterfactual Explanations: a Theoretical Analysis' abstract: 'Since the introduction of SHAP, many methods adapted the idea of using the {Shapley} value formula as a way to measure the importance of a feature in the decision of a model. However, computing this value theoretically imply to relearn the model with and without the feature for all subsets of features. To avoid this, the methods rely on sampling to compute an expectation to measure a mean impact of a feature. In this paper we investigate theoretically if we could, and under which conditions, build and use a textbook cooperative game with the help of other explanation techniques, Prime Implicants and Counterfactual explanations, for computing {Shapley} values for interpretability. We propose detailed and iterative analysis of the number of remaining explanations during the enumeration of the explanations, alongside the computation of the {Shapley} value and its upper and lower bounds.' volume: 337 URL: https://proceedings.mlr.press/v337/willot26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/willot26a/willot26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-willot26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Hénoïk family: Willot editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7387-7402 id: willot26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7387 lastpage: 7402 published: 2026-08-06 00:00:00 +0000 - title: 'An NTK Theory Approach to UCB Estimation in Semi-gradient TD Learning' abstract: 'Efficient exploration is a central challenge in reinforcement learning ({RL}), especially under sparse rewards, large state-action spaces, or adversarial environment dynamics. A principled approach to exploration is to choose actions that maximize the upper bound return. Under certain conditions, this can be formulated in the {Bayesian} framework as exploration based on the posterior variance. In practice, the predictive variance of a neural network is often used as a surrogate for the posterior variance by techniques such as ensembles, randomized priors, and random network distillation. However, for wide neural networks, neural tangent kernel ({NTK}) theory proves there is a discrepancy between the predictive variance of a wide neural network trained by gradient descent and its posterior variance. This is a known issue in supervised learning and there exist methods to reconcile this discrepancy. In this work, we show that, in contrast to the supervised setting, reconciliation is not possible for semi-gradient temporal difference ({TD}) learning, which is a commonly used algorithm in deep {RL}. Instead, we derive the upper confidence bound ({UCB}) of the value function in semi-gradient {TD} learning directly and show that this {UCB} can be estimated by a neural network. To aid our analysis, we extend {NTK} theory to regularized semi-gradient {TD} learning.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26a/wu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yijun family: Wu - given: Pascal R. prefix: van der family: Vaart - given: Moritz Akiya family: Zanger - given: Matthijs T. J. family: Spaan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7403-7415 id: wu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7403 lastpage: 7415 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Representations from Perturbation: A Novel Matrix-View Weighting Framework for Naive Bayes' abstract: 'Numerous attribute weighting methods have recently been proposed to alleviate the attribute conditional independence assumption in naive {Bayes}. Among them, multi-view attribute weighting framework has achieved state-of-the-art performance by constructing additional latent views beyond the raw attribute view, thereby capturing more comprehensive data characteristics. However, these latent views are usually derived from base classifiers trained on a fixed input distribution, which greatly limits the diversity of generated attributes. Additionally, in most cases, the latent views consist solely of hard labels, disregarding the predicted posterior probability of the base classifiers, resulting in incomplete utilization of discriminative evidence. To address these issues, we propose a novel framework called Perturbation-driven Matrix-view Weighted Naive {Bayes} (PMWNB). In PMWNB, diverse input perturbations are first applied to the raw attribute view to generate multiple base views. Subsequently, each base view independently trains multiple heterogeneous base classifiers, whose hard label and soft probability outputs are jointly leveraged to construct four latent views. Finally, class-specific attribute value weights in each view are respectively optimized by minimizing the negative conditional log-likelihood. Extensive experiments conducted on a collection of 59 benchmark datasets demonstrate the superiority of PMWNB. The source code and datasets are available at https://github.com/zhanghuan1994/PMWNB.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26b/wu26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Siyao family: Wu - given: Huan family: Zhang - given: Kexin family: Meng - given: Zhipeng family: Ding - given: Pei family: Lv editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7416-7432 id: wu26b issued: date-parts: - 2026 - 8 - 6 firstpage: 7416 lastpage: 7432 published: 2026-08-06 00:00:00 +0000 - title: 'On the Convergence of Self-Improving Online LLM Alignment' abstract: 'The Self-Improving Alignment (SAIL) algorithm addresses distribution shift by reducing a bilevel formulation of the problem to an efficient, single-level method. Empirically, SAIL has demonstrated strong performance on this task. However, a formal analysis of its convergence properties has been lacking. We identify a key theoretical challenge: the standard SAIL objective function is not guaranteed to be strongly concave due to unfavorable properties of its Hessian. To address this limitation, we propose a regularized objective, SAIL-RevKL, which incorporates a reverse Kullback-Leibler (KL) divergence penalty to improve the optimization landscape. Our central theoretical contribution is to prove that this regularized objective satisfies the {Polyak-Lojasiewicz} (PL) condition within a bounded parameter space. We establish global convergence guarantees, achieving a near-linear sample complexity. We further validate the effectiveness and stability of SAIL-RevKL through empirical evaluations, demonstrating that it outperforms the vanilla SAIL on both MuJoCo benchmarks and {LLM} alignment tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26c/wu26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xudong family: Wu - given: Pangpang family: Liu - given: Vaneet family: Aggarwal - given: Jiayu family: Chen editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7433-7467 id: wu26c issued: date-parts: - 2026 - 8 - 6 firstpage: 7433 lastpage: 7467 published: 2026-08-06 00:00:00 +0000 - title: 'Concept Sketching for Description Logics' abstract: 'Domain experts often know *part* of a target description logic (DL) concept (a conjunction involving an existential restriction here, a structural pattern there), yet every existing concept learner ignores this knowledge and searches from scratch. We introduce *concept sketching* for the DL $\mathcal{ALC}$: the expert supplies a partial formula with typed holes (unknown subconcepts, unary or binary constructors), and any suitable back-end learner completes it from labeled examples. This *sketch fitting* problem turns out to have a sharp complexity landscape governed by a single dividing line: the signature size $|\Sigma|$. The problem is NP-complete even for a single hole; with $|\Sigma|$ as parameter it becomes fixed-parameter tractable; but without $|\Sigma|$ it is W[2]-hard, except for Type-2-only sketches which remain tractable. This dichotomy parallels recent results in first-order and decision tree learning. On the statistical side, we prove that each hole type contributes independently to {PAC} sample complexity, with a matching lower bound, so that a sketch capturing even part of the target structure requires provably fewer examples than unrestricted bounded fitting. Experiments on five standard DL benchmarks with two fundamentally different back-ends (SAT-based fitting and evolutionary concept learning) confirm improved accuracy, sample efficiency, and solver speed, demonstrating that sketching benefits are learner-agnostic.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26d/wu26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jinghan family: Wu - given: Chang family: Lu - given: Renate family: Schmidt - given: Yizheng family: Zhao editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7468-7483 id: wu26d issued: date-parts: - 2026 - 8 - 6 firstpage: 7468 lastpage: 7483 published: 2026-08-06 00:00:00 +0000 - title: 'DRL-ORA: Distributional Reinforcement Learning with Online Epistemic Risk Adaptation' abstract: 'One of the main challenges in reinforcement learning ({RL}) is that the agent has to make decisions that would influence the future performance without having complete knowledge of the environment. Dynamically adjusting the level of epistemic risk during the learning process can help to achieve reliable policies in safety-critical settings with better efficiency. In this work, we propose a new framework, Distributional {RL} with Online Epistemic Risk Adaptation ({DRL-ORA}). This framework quantifies both epistemic and implicit aleatory uncertainties in a unified manner and dynamically adjusts the epistemic risk levels by solving a total variation minimization problem online. The framework generalizes the existing variants of risk adaptation approaches with better explainability and flexibility. The selection of risk levels is performed efficiently via a Follow-The-Leader-type algorithm. We show that {DRL-ORA} outperforms existing methods that rely on fixed risk levels or manually designed risk level adaptation in multiple classes of tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26e/wu26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yupeng family: Wu - given: Wenyun family: Li - given: Wenjie family: Huang - given: Chin Pang family: Ho editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7484-7503 id: wu26e issued: date-parts: - 2026 - 8 - 6 firstpage: 7484 lastpage: 7503 published: 2026-08-06 00:00:00 +0000 - title: 'Federated Combinatorial Causal Bandits with Heterogeneous Causal Influences' abstract: 'We explore the problem of federated combinatorial causal bandits (FedCCB), where multiple agents collaboratively select variables for intervention and gather feedback. The primary objective of FedCCB is to identify optimal interventions for each agent while minimizing the total cumulative regret associated with the target nodes. A key challenge in FedCCB stems from the inherent heterogeneity of local causal models, which often exhibit diverse causal influences. To address this challenge, we propose a novel Federated Subset-Clustered Bandit (FedSCuB) method. This method groups agents to tackle heterogeneity based on the similarity of their causal relationships with specified subsets of variables. FedSCuB incorporates an intervention-based exploration strategy to collect partial observations necessary for clustering, as well as an alternating minimization method to facilitate collaboration among agents within the same cluster. Theoretical analysis demonstrates that the proposed FedSCuB method achieves sub-linear regret and offers a better regret bound compared to baseline methods. Empirical evaluations on synthetic tasks further confirm the effectiveness and superiority of our method.' volume: 337 URL: https://proceedings.mlr.press/v337/wu26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/wu26f/wu26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-wu26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zheshun family: Wu - given: Wei family: Chen - given: Zenglin family: Xu - given: Fang family: Kong editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7504-7535 id: wu26f issued: date-parts: - 2026 - 8 - 6 firstpage: 7504 lastpage: 7535 published: 2026-08-06 00:00:00 +0000 - title: 'ARGUS: Argumentation-Based Minimal-Change Repair for Verifiable LLM Self-Explanations' abstract: 'When large language models produce natural-language rationales, those explanations are frequently unfaithful to the model’s actual reasoning—and no existing framework provides a principled way to repair them when new evidence arrives. We introduce ARGUS, a framework that structures {LLM} self-explanations as Dung-style abstract argumentation frameworks and verifies them under grounded and preferred semantics. When new or uncertain evidence renders an explanation inconsistent, ARGUS computes a minimum-cost set of edit operations that restores the desired acceptability status of the target argument. The repair operator satisfies adapted AGM revision postulates and is bidirectionally characterized by them (Representation Theorem): the decision problem is in P under grounded semantics, NP-complete under preferred and stable semantics, and $\Sigma_2^P$-complete under skeptical stable semantics. A $k$-neighborhood approximation and an answer set programming (ASP) encoding ensure scalability to practical framework sizes. We validate the framework on HotpotQA and FEVER, where ARGUS achieves relative improvements of 10.3% in faithfulness and 14.5% in contestability over the strongest argumentation baseline while requiring fewer repair operations than all repair-capable competing methods.' volume: 337 URL: https://proceedings.mlr.press/v337/xiao26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xiao26a/xiao26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xiao26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yifan family: Xiao - given: Shijie family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7536-7551 id: xiao26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7536 lastpage: 7551 published: 2026-08-06 00:00:00 +0000 - title: 'Improving online FDR procedures via online analogs of e-closure and compound e-values' abstract: 'In many scientific applications, hypotheses are generated and tested continuously in a stream. We develop a framework for improving online multiple testing procedures with false discovery rate ({FDR}) control under arbitrary dependence. Our approach is two-fold: we construct methods via the online e-closure principle, as well as a novel formulation in online compound e-values constructed via donations. This yields strict power improvements over state-of-the-art e-value and p-value procedures while retaining {FDR} control. We further derive algorithms that compute the rejection decision at time $t$ in $O(\log t)$ time, and we demonstrate improved empirical performance on synthetic and real data.' volume: 337 URL: https://proceedings.mlr.press/v337/xu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xu26a/xu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ziyu family: Xu - given: Lasse family: Fischer - given: Aaditya family: Ramdas editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7552-7561 id: xu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7552 lastpage: 7561 published: 2026-08-06 00:00:00 +0000 - title: 'How Learning Dynamics Drive Adversarially Robust Generalization?' abstract: 'Despite being widely adopted as a canonical framework for learning robust models, adversarial training suffers from robust overfitting. Existing empirical and theoretical explorations fail to provide a satisfactory mechanistic interpretation of the phenomenon. By modeling adversarial training with momentum {SGD} as a discrete-time dynamical system, we propose a {PAC}-{Bayesian} analytical framework that proves time-resolved robust generalization bounds. Specifically, our framework tracks the closed-form evolution of the posterior mean and covariance under both stationary and non-stationary transient regimes, connecting the model’s robust generalization performance to learning rate, local loss geometry, and mini-batch stochastic gradients. By estimating the key quantities associated with the bound, we illustrate the underlying mechanism of robust overfitting. Our framework also shows how adversarial weight perturbation reduces robust generalization gaps by suppressing dominant loss-curvature modes, while suggesting that excessive penalization can be sub-optimal for optimization.' volume: 337 URL: https://proceedings.mlr.press/v337/xu26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xu26b/xu26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xu26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuelin family: Xu - given: Xiao family: Zhang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7562-7593 id: xu26b issued: date-parts: - 2026 - 8 - 6 firstpage: 7562 lastpage: 7593 published: 2026-08-06 00:00:00 +0000 - title: 'Kronecker-Structured Nonparametric Spatiotemporal Point Processes' abstract: 'Events in spatiotemporal domains arise in numerous real-world applications, where uncovering event relationships and enabling accurate prediction are central challenges. Classical {Poisson} and Hawkes processes rely on restrictive parametric assumptions that limit their ability to capture complex interaction patterns, while recent neural point process models increase representational capacity but integrate event information in a black-box manner, hindering interpretable relationship discovery. To address these limitations, we propose a Kronecker-Structured Nonparametric Spatiotemporal Point Process (KSTPP) that enables transparent event-wise relationship discovery while retaining high modeling flexibility. We model the background intensity with a spatial {Gaussian} process (GP) and the influence kernel as a spatiotemporal GP, allowing rich interaction patterns including excitation, inhibition, neutrality, and time-varying effects. To enable scalable training and prediction, we adopt separable product kernels and represent the GPs on structured grids, inducing Kronecker-structured covariance matrices. Exploiting Kronecker algebra substantially reduces computational cost and allows the model to scale to large event collections. In addition, we develop a tensor-product Gauss-Legendre quadrature scheme to efficiently evaluate intractable likelihood integrals. Extensive experiments demonstrate the effectiveness of our framework.' volume: 337 URL: https://proceedings.mlr.press/v337/xu26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xu26c/xu26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xu26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhitong family: Xu - given: Qiwei family: Yuan - given: Yinghao family: Chen - given: Yan family: Sun - given: Bin family: Shen - given: Shandian family: Zhe editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7594-7612 id: xu26c issued: date-parts: - 2026 - 8 - 6 firstpage: 7594 lastpage: 7612 published: 2026-08-06 00:00:00 +0000 - title: 'Efficient Q-Learning and Actor–Critic Methods for Robust Average-Reward Reinforcement Learning.' abstract: 'We study model-free methods for distributionally robust infinite-horizon average-reward {Markov} decision processes ({MDPs}). We present non-asymptotic convergence analyses of $Q$-learning and actor–critic algorithms for robust average-reward {MDPs} under contamination, total-variation distance, and {Wasserstein} uncertainty sets. A key ingredient of our analysis is showing that the optimal robust {Bellman} operator is a strict contraction with respect to a carefully designed semi-norm. This property enables a stochastic approximation update that learns the optimal robust $Q$-function using $\tilde{\mathcal{O}}(\epsilon^{-2})$ samples. We also establish robust {TD} convergence bounds whose constants are uniform over all stationary policies, yielding an efficient data-driven routine for robust critic estimation. Building on this, we introduce an actor–critic algorithm that learns an $\epsilon$-optimal robust policy within $\tilde{\mathcal{O}}(\epsilon^{-2})$ samples. We provide numerical simulations to illustrate the qualitative behavior of the proposed algorithms. Our results contribute to the theoretical foundations of robust planning under model misspecification, and to model-free approaches for building robust long-run policies directly from simulation data.' volume: 337 URL: https://proceedings.mlr.press/v337/xu26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xu26d/xu26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xu26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yang family: Xu - given: Swetha family: Ganesh - given: Vaneet family: Aggarwal editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7613-7650 id: xu26d issued: date-parts: - 2026 - 8 - 6 firstpage: 7613 lastpage: 7650 published: 2026-08-06 00:00:00 +0000 - title: 'Implicit Variational Rejection Sampling' abstract: 'Variational Inference (VI) is a fundamental inference technique in {Bayesian} machine learning for approximating complex posterior distributions. Traditional VI often relies on the mean-field factorization, which can inadequately capture true posterior complexity. Recent advancements have leveraged neural networks to model implicit distributions, offering increased flexibility. However, the practical constraints of neural network architectures still produces inaccuracies. In this paper, we propose a method called Implicit Variational Rejection Sampling (IVRS), which integrates implicit distributions with rejection sampling to improve the posterior approximation. Our method uses neural networks to construct implicit proposal distributions, and rejection sampling with a discriminator network that estimates the density ratio between the implicit proposal and the true posterior for refining the approximation. Towards this end, we introduce the Implicit Resampling Evidence Lower Bound (IR-{ELBO}) as a metric to characterize the resampled distribution’s quality and derive a tighter variational lower bound. Experimental results demonstrate that our method outperforms traditional variational inference techniques.' volume: 337 URL: https://proceedings.mlr.press/v337/xu26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/xu26e/xu26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-xu26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jian family: Xu - given: Shigui family: Li - given: Wei family: Chen - given: Jiacheng family: Li - given: Zhiqi family: Lin - given: Delu family: Zeng - given: Xinghao family: Ding - given: John family: Paisley - given: Qibin family: Zhao editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7651-7669 id: xu26e issued: date-parts: - 2026 - 8 - 6 firstpage: 7651 lastpage: 7669 published: 2026-08-06 00:00:00 +0000 - title: 'Vanilla SGD with Momentum Survives Heavy-Tailed Noise: Convergence Analysis without Gradient Clipping or Normalization' abstract: 'Stochastic Gradient Descent ({SGD}) is a cornerstone of modern optimization. While its performance under heavy-tailed noise is often addressed through specialized modifications such as gradient clipping or normalization, we investigate a more fundamental question: how does vanilla {SGD}, particularly with momentum, perform in the presence of heavy-tailed noise? In this paper, we refine existing convergence results for vanilla {SGD} and, more importantly, provide the first comprehensive convergence analysis of vanilla {SGD} with momentum for strongly convex, convex, and nonconvex objectives, without employing any gradient control mechanisms. Our results demonstrate that the obtained convergence rates are inferior to the optimal rates achieved by clipped or normalized variants of {SGD}, thereby revealing inherent limitations of vanilla methods under heavy-tailed noise. The theoretical findings are supported by experiments on synthetic functions.' volume: 337 URL: https://proceedings.mlr.press/v337/yamada26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yamada26a/yamada26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yamada26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ryusei family: Yamada - given: Naoki family: Sato - given: Hideaki family: Iiduka editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7670-7700 id: yamada26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7670 lastpage: 7700 published: 2026-08-06 00:00:00 +0000 - title: 'Robust Decision-Focused Learning via Worst-Case Regret Minimization' abstract: 'In optimization-based decision-making, when the objective coefficient vector is unknown, a common approach is to predict it from covariates using a machine learning model and solve the downstream optimization problem. However, improving predictive accuracy does not necessarily lead to better decisions. This has motivated Decision-Focused Learning (DFL), which trains predictive models to minimize decision loss measured by regret. Despite recent progress, existing DFL methods do not sufficiently address two sources of uncertainty: (i) observation errors in the measured coefficients, and (ii) distribution shift in the coefficient vector at deployment due to environmental changes. These uncertainties can degrade solution quality. In this paper, we propose two robust regret losses to address these uncertainties. For uncertainty (i), we introduce an uncertainty set around the observed coefficient vector that captures measurement errors and define the loss as the worst-case regret over this set. For uncertainty (ii), we construct a {Wasserstein} ambiguity set around the conditional empirical distribution and define the loss using the worst-case distribution within the set. We enable efficient training via Danskin-based subgradients. Experiments demonstrate that our method reduces regret and yields more stable solutions than existing robust DFL approaches.' volume: 337 URL: https://proceedings.mlr.press/v337/yamao26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yamao26a/yamao26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yamao26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Shoki family: Yamao - given: Ken family: Kobayashi - given: Ryo family: Matsui - given: Shota family: Nagai - given: Naoki family: Nishimura - given: Kazuhide family: Nakata editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7701-7736 id: yamao26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7701 lastpage: 7736 published: 2026-08-06 00:00:00 +0000 - title: 'One-Shot Federated Learning based on Random Feature Extractor' abstract: 'The transition from multi-rounds federated learning to one-shot federated learning (OFL) markedly alleviates communication burden and represents a major step toward realistic deployment. Most existing OFL approaches require clients to perform local training, imposing a substantial computational burden on client side, while others rely on pre-trained models. In this paper, we propose a novel one-shot federated learning framework based on random feature extractor (FedRFE). Unlike existing approaches, it does not require any local model training or pre-trained model, featuring superior resource efficiency. Through comprehensive experiments, we show FedRFE achieves competitive performance while being robust in challenging scenarios including data heterogeneity and client scalability. Our code is available at\url{https://github.com/luyuanxyang/FedRFE}' volume: 337 URL: https://proceedings.mlr.press/v337/yang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26a/yang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Luyuan family: Yang - given: Shayan family: Shafaei - given: Yiming family: Liu - given: Naeem family: Shahabi Sani - given: Yu family: Cai - given: Jun family: Huan - given: Chao family: Lan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7737-7750 id: yang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7737 lastpage: 7750 published: 2026-08-06 00:00:00 +0000 - title: 'ReVAD: From Imitation to Reasoning in Vectorized Autonomous Driving via Latent Space Search' abstract: 'Vectorized end-to-end (E2E) autonomous driving models predominantly rely on reactive imitation learning. By failing to model underlying environmental dynamics, these agents lack counterfactual reasoning capabilities and struggle with uncertainty in out-of-distribution ({OOD}) scenarios. To bridge the gap between reactive imitation and deliberative decision-making, we introduce Reasoning-enhanced VAD ({ReVAD}), empowering agents with a “System 2” cognitive framework via Latent Space Search. Unlike computationally expensive pixel-level world models, {ReVAD} integrates a probabilistic Token Dynamics Model with Latent Monte Carlo Tree Search to perform efficient lookahead planning entirely within a sparse semantic token space. By simulating future states to evaluate risk and utilizing imitation policies solely as search priors, {ReVAD} effectively mitigates the distribution shift inherent in pure imitation learning, demonstrating significantly improved robustness and safety in high-uncertainty environments.' volume: 337 URL: https://proceedings.mlr.press/v337/yang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26b/yang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhao family: Yang - given: Chengkang family: Duan - given: Weiyi family: Hu - given: Haoran family: Hu - given: Hua family: Cui - given: Qingshuang family: Sun editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7751-7760 id: yang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 7751 lastpage: 7760 published: 2026-08-06 00:00:00 +0000 - title: 'Verbalizing LLM’s Higher-order Uncertainty via Imprecise Probabilities' abstract: 'Despite the growing demand for eliciting uncertainty from large language models ({LLMs}), empirical evidence suggests that {LLM} behavior is not always adequately captured by the elicitation techniques developed under the classical probabilistic uncertainty framework. This mismatch leads to systematic failure modes, particularly in settings that involve ambiguous question-answering, in-context learning, and self-reflection. To address this, we propose novel prompt-based uncertainty elicitation techniques grounded in *imprecise probabilities*, a principled framework for representing and eliciting higher-order uncertainty. Here, first-order uncertainty captures uncertainty over possible responses to a prompt, while second-order uncertainty (uncertainty about uncertainty) quantifies indeterminacy in the underlying probability model itself. We introduce general-purpose prompting and post-processing procedures to directly elicit and quantify both orders of uncertainty, and demonstrate their effectiveness across diverse settings. Our approach enables more faithful uncertainty reporting from {LLMs}, improving credibility and supporting downstream decision-making.' volume: 337 URL: https://proceedings.mlr.press/v337/yang26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26c/yang26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yang26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Anita family: Yang - given: Krikamol family: Muandet - given: Michele family: Caprio - given: Siu Lun family: Chau - given: Masaki family: Adachi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7761-7779 id: yang26c issued: date-parts: - 2026 - 8 - 6 firstpage: 7761 lastpage: 7779 published: 2026-08-06 00:00:00 +0000 - title: 'Evaluating the Role of Great Pre-trained Diffusion Models in Few-shot Phase: Warm-up and Acceleration' abstract: 'Due to the customized requirements, few-shot diffusion models have attracted much attention. However, only a few works analyze few-shot models, and none involve the fast few-shot optimization process, which is important for quickly responding to users. In this work, we evaluate the role of each operation in the optimization process and prove the convergence guarantee for few-shot diffusion models. A standard operation for the few-shot model is only fine-tuning some key parameters to avoid overfitting the limited target dataset. We first show that this operation is insufficient from empirical and theoretical perspectives. Empirically, we conduct real-world few-shot fine-tuning experiments with underfitting and overfitting bad pre-trained models and show that the results are heavily influenced by these bad models. Theoretically, we also prove that the few-shot phase can not learn the ground-truth parameters and suffers from a small gradient when using a bad pre-trained model. Based on these results, we highlight the importance of a great pre-trained model by showing it can warm up few-shot models and lead to a strongly convex landscape for few-shot diffusion models. As a result, the few-shot model fast converges to the ground-truth parameters. In contrast, we show that with a bad initialization, the pretraining phase requires large optimization steps to converge.' volume: 337 URL: https://proceedings.mlr.press/v337/yang26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26d/yang26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yang26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ruofeng family: Yang - given: Yongcan family: Li - given: Bo family: Jiang - given: Cheng family: Chen - given: Shuai family: Li editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7780-7817 id: yang26d issued: date-parts: - 2026 - 8 - 6 firstpage: 7780 lastpage: 7817 published: 2026-08-06 00:00:00 +0000 - title: 'Near-Exponential Convergence Rates for kNN Classifications based on Boltzmann Margin' abstract: 'Convergence-rate analysis for classifiers is often conducted under either Tsybakov margin or Massart margin. The former is a relatively weak condition that typically yields polynomial rates, while the latter is substantially stronger but can guarantee exponential rates. In this paper, we introduce a new condition, called *Boltzmann margin*, that bridges the gap between these two regimes. It is weaker than Massart margin, generally stronger than Tsybakov margin, and can imply many of their properties under suitable conditions. We apply Boltzmann margin to the analysis of kNN classifiers and establish the first *near-exponential* convergence rates for kNN classification. We also present extensions of the main results and provide numerical evidence supporting the main theoretical implications.' volume: 337 URL: https://proceedings.mlr.press/v337/yang26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yang26e/yang26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yang26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Luyuan family: Yang - given: Shayan family: Shafaei - given: Chao family: Lan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7818-7837 id: yang26e issued: date-parts: - 2026 - 8 - 6 firstpage: 7818 lastpage: 7837 published: 2026-08-06 00:00:00 +0000 - title: 'When Can Transformers Count to n?' abstract: 'Large language models based on the transformer architecture can solve highly complex tasks, yet their fundamental limitations on simple algorithmic problems remain poorly understood. In this work, we focus on basic counting tasks and investigate how the difficulty of these tasks scales with the transformer embedding dimension, the context length, and the vocabulary size. We reveal a sharp theoretical phase transition governed by the relationship between the embedding dimension and the vocabulary size. When the dimension is at least as large as the vocabulary, transformers can perfectly maintain token counts. However, when the vocabulary exceeds the embedding dimension, the interference between non-orthogonal token representations forces the network weights to scale polynomially. This renders the exact counting algorithm numerically unstable and practically unlearnable. We empirically validate this bottleneck by training transformers from scratch, demonstrating a strict performance drop at the theoretical threshold and catastrophic out of distribution failure when scaling the vocabulary or context length. Furthermore, we show that state-of-the-art pretrained models suffer from similar failure cases. Our work reveals a critical blind spot absent from the current literature regarding the connection among these three parameters, proving that vocabulary size fundamentally dictates the difficulty of counting tasks.' volume: 337 URL: https://proceedings.mlr.press/v337/yehudai26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yehudai26a/yehudai26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yehudai26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Gilad family: Yehudai - given: Haim family: Kaplan - given: Guy family: Dar - given: Royi family: Rassin - given: Asma family: Ghandeharioun - given: Mor family: Geva - given: Amir family: Globerson editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7838-7855 id: yehudai26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7838 lastpage: 7855 published: 2026-08-06 00:00:00 +0000 - title: 'Estimating Interventional Outcomes over Time with Causal Normalizing Flow' abstract: 'Estimating outcome distributions under time-varying treatments is an essential task for personalized decision-making, particularly in domains such as healthcare. Most prior work in this area focuses on point predictions, which fail to capture the inherent variability in outcomes. Recent efforts in causal inference have begun integrating generative models to address this limitation by estimating interventional distributions. However, existing approaches—including causal normalizing flows—are generally restricted to static settings and are not well suited to sequential, time-dependent data. In this work, we propose a novel framework that extends causal normalizing flows to time-series, enabling simulation-based interventional density estimation over time. Our method learns representations of treatment and covariate history that capture temporal dependencies. Conditioned on these representations and guided by a causal graph, our flow-based model generates interventional samples, allowing for the simulation of outcome trajectories under alternative treatment strategies. We evaluate our approach on both linear and non-linear synthetic time-series as well as on a simulated tumor growth dataset, demonstrating that it achieves performance competitive with state-of-the-art baselines, while accommodating a broader spectrum of causal queries.' volume: 337 URL: https://proceedings.mlr.press/v337/yeom26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yeom26a/yeom26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yeom26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yoonseok family: Yeom - given: Jonghwan family: Kim - given: Taehui family: Yun - given: Juhyun family: Lyu - given: Jung-Hee family: Kim - given: Sangmin family: Lee - given: Jinseok family: Yang - given: Hyemin family: Jung - given: Woohyung family: Lim - given: Sanghack family: Lee editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7856-7895 id: yeom26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7856 lastpage: 7895 published: 2026-08-06 00:00:00 +0000 - title: 'Neural Value Iteration' abstract: 'The value function of a POMDP exhibits the piecewise-linear-convex (PWLC) property and can be represented as a finite set of hyperplanes, known as $\alpha$-vectors. Most state-of-the-art POMDP solvers (offline planners) follow the point-based value iteration scheme, which performs {Bellman} backups on $\alpha$-vectors at reachable belief points until convergence. However, since each $\alpha$-vector is $|S|$-dimensional, these methods quickly become intractable for large-scale problems due to the prohibitive computational cost of {Bellman} backups. In this work, we demonstrate that the PWLC representation of POMDP value functions can be generalized by replacing the alpha-vector sets with a finite set of neural networks. This insight enables a novel POMDP planning algorithm, called *Neural Value Iteration*, which combines the generalization capability of neural networks with the classical value iteration framework. Requiring only a black-box simulator, our approach scales to extremely large POMDPs that are intractable for existing offline solvers.' volume: 337 URL: https://proceedings.mlr.press/v337/you26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/you26a/you26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-you26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yang family: You - given: Ufuk family: \textÇakır - given: Alex family: Schutz - given: Nick family: Hawes editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7896-7912 id: you26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7896 lastpage: 7912 published: 2026-08-06 00:00:00 +0000 - title: 'MMG: Mutual Information Estimation via the MMSE Gap in Diffusion' abstract: 'Mutual information is one of the most general ways to measure relationships between random variables, but estimating this quantity for complex systems is challenging. Denoising diffusion models have recently set a new bar for density estimation, so it is natural to consider whether these methods could also be used to improve mutual information estimation. Using the recently introduced information-theoretic formulation of denoising diffusion models, we show that diffusion models can be used in a straightforward way to estimate mutual information. In particular, the mutual information corresponds to half the gap in the minimum mean square error between conditional and unconditional diffusion, integrated over all signal-to-noise ratios in the noising process. Our approach not only passes self-consistency tests but also outperforms traditional and score-based diffusion estimators. Furthermore, our method leverages adaptive importance sampling to achieve scalable estimation, while maintaining strong performance even when the mutual information is high. Code to reproduce our experiments is available at \url{https://github.com/fengsxy/Diffusion_MI}, and the unified mutual information estimation library is available at \url{https://github.com/fengsxy/Diffusion-MI}.' volume: 337 URL: https://proceedings.mlr.press/v337/yu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/yu26a/yu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-yu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Longxuan family: Yu - given: Xing family: Shi - given: Xianghao family: Kong - given: Tong family: Jia - given: Greg family: Ver Steeg editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7913-7927 id: yu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7913 lastpage: 7927 published: 2026-08-06 00:00:00 +0000 - title: 'Optimizing Likelihoods via Mutual Information: Bridging Simulation-Based Inference and Bayesian Optimal Experimental Design' abstract: 'Simulation-based inference (SBI) depends on expensive simulators, so inference and experimental design must operate under fixed simulation budgets. {Bayesian} optimal experimental design (BOED) maximizes expected information gain (EIG), but is often implemented with a separate mutual-information critic, used only as a diagnostic, or restricted to differentiable simulators. We show that the InfoNCE lower bound on EIG becomes a principled SBI training objective when the critic is a normalized conditional density model. Maximizing the bound is equivalent to fitting a surrogate likelihood by minimizing a KL divergence plus a marginal-likelihood term, so each simulator call can improve both inference and design. We propose SBI-BOED, a single stochastic-gradient procedure that jointly trains a conditional normalizing-flow likelihood and optimizes designs without simulator differentiability. The same MI view also yields simulation active learning under fixed designs via epistemic predictive information gain (EPIG). With an InfoNCE-$\lambda$ objective and practical stabilizers, SBI-BOED improves posterior calibration and predictive accuracy over strong BOED baselines on synthetic benchmarks and scientific simulators at matched simulation budgets.' volume: 337 URL: https://proceedings.mlr.press/v337/zaballa26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zaballa26a/zaballa26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zaballa26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Vincent D. family: Zaballa - given: Elliot E family: Hui editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7928-7951 id: zaballa26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7928 lastpage: 7951 published: 2026-08-06 00:00:00 +0000 - title: 'On the Equivalence of Random Network Distillation, Deep Ensembles, and Bayesian Inference' abstract: 'Uncertainty quantification is central to safe and efficient deployments of deep learning models, yet many computationally practical methods lack lacking rigorous theoretical motivation. Random network distillation (RND) is a lightweight technique that measures novelty via prediction errors against a fixed random target. While empirically effective, it has remained unclear what uncertainties RND measures and how its estimates relate to other approaches, e.g., {Bayesian} inference or deep ensembles. We establish these missing theoretical connections by analyzing RND within the neural tangent kernel framework in the limit of infinite network width. Our analysis reveals two central findings in this limit: (1) The uncertainty signal from RND—its squared self-predictive error—is equivalent to the predictive variance of a deep ensemble. (2) By constructing a specific RND target function, we show that the RND error distribution can be made to mirror the centered posterior predictive distribution of {Bayesian} inference with wide neural networks. Based on this equivalence, we moreover devise a posterior sampling algorithm that generates i.i.d. samples from an exact {Bayesian} posterior predictive distribution using this modified \textit{{Bayesian} RND} model. Collectively, our findings provide a unified theoretical perspective that places RND within the principled frameworks of deep ensembles and {Bayesian} inference, and offer new avenues for efficient yet theoretically grounded uncertainty quantification methods.' volume: 337 URL: https://proceedings.mlr.press/v337/zanger26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zanger26a/zanger26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zanger26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Moritz Akiya family: Zanger - given: Yijun family: Wu - given: Pascal R. prefix: van der family: Vaart - given: Wendelin family: Böhmer - given: Matthijs T. J. family: Spaan editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7952-7976 id: zanger26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7952 lastpage: 7976 published: 2026-08-06 00:00:00 +0000 - title: 'A Debiased LASSO Estimator for Design Matrices with Non-zero Mean Elements' abstract: 'The {LASSO} estimator has been popular in diverse fields such as statistics, bio-informatics and compressed sensing for estimation of sparse signals from under-sampled measurements. As the {LASSO} does not provide confidence intervals for the estimates of the individual elements, techniques such as the debiased {LASSO} have been developed that provide such confidence intervals and also mitigate the inherent bias in the {LASSO} estimates. However the theoretical guarantees underlying the debiased {LASSO} have been developed for a design or measurement matrix whose elements have zero mean. On the other hand, many commonly used measurement matrices in sparse regression applications in optical imaging or pooled biological testing involve non-negative, particularly binary, matrices whose elements have a non-zero mean. In this paper, we propose a debiased {LASSO} technique based on computing differences between different row subsets of the underlying design matrix iteratively which effectively converts the design matrix into one with zero-mean elements. We show analytically that this results in lower variances for the individual elements of the debiased {LASSO} estimate as compared to the standard debiased {LASSO}. We also provide numerical results to support our theory.' volume: 337 URL: https://proceedings.mlr.press/v337/zantye26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zantye26a/zantye26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zantye26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ashish family: Zantye - given: Ajit family: Rajwade - given: Radhendushka family: Srivastava editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7977-7991 id: zantye26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7977 lastpage: 7991 published: 2026-08-06 00:00:00 +0000 - title: 'Structural Drift Repair in Decision Trees via Bayesian Model-Based Diagnosis' abstract: 'Decision trees are widely used in machine learning due to their interpretability. However, when the underlying data distribution changes—a phenomenon known as concept drift—their performance can degrade significantly. Retraining the model from scratch discards the learned structure and offers no insight into which nodes were actually affected. Prior work, APPETITE, used spectrum-based fault localization to identify and modify a single faulty node, but cannot handle drift that affects multiple nodes simultaneously or that demands structural changes to the tree. We propose BTAD ({Bayesian} Tree Adaptation for Drift), which formalizes the Decision Tree Concept Drift Problem as a Model-Based Diagnosis task and employs BARINEL, a {Bayesian} algorithm that ranks multi-node fault hypotheses across the entire tree. For repair, BTAD applies Subtree Re-fitting, replacing affected subtrees with ones fitted to the post-drift distribution. BTAD relies on lightweight node-level statistics and requires no access to the original training data. Experiments show that BTAD outperforms APPETITE in both recovery and localization, achieving accuracy comparable to full retraining—which provides no drift insight and requires the original data.' volume: 337 URL: https://proceedings.mlr.press/v337/zelinger26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zelinger26a/zelinger26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zelinger26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yoav family: Zelinger - given: Meir family: Kalech editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 7992-8005 id: zelinger26a issued: date-parts: - 2026 - 8 - 6 firstpage: 7992 lastpage: 8005 published: 2026-08-06 00:00:00 +0000 - title: 'ALIGN: Adversarial Learning for Generalizable Speech Neuroprosthesis' abstract: 'Intracortical brain-computer interfaces (BCIs) can decode speech from neural activity with high accuracy when trained on data pooled across recording sessions. In realistic deployment, however, models must generalize to new sessions without labeled data, and performance often degrades due to cross-session nonstationarities (e.g., electrode shifts, neural turnover, and changes in user strategy). In this paper, we propose {ALIGN}, a session-invariant learning framework based on multi-domain adversarial neural networks for semi-supervised cross-session adaptation. {ALIGN} trains a feature encoder jointly with a phoneme classifier and a domain classifier operating on the latent representation. Through adversarial optimization, the encoder is encouraged to preserve task-relevant information while suppressing session-specific cues. We evaluate {ALIGN} on intracortical speech decoding and find that it generalizes consistently better to previously unseen sessions, improving both phoneme error rate and word error rate relative to baselines. These results indicate that adversarial domain alignment is an effective approach for mitigating session-level distribution shift and enabling robust longitudinal BCI decoding.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26a/zhang26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhanqi family: Zhang - given: Shun family: Li - given: Bernardo L. family: Sabatini - given: Mikio Christian family: Aoi - given: Gal family: Mishne editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8006-8025 id: zhang26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8006 lastpage: 8025 published: 2026-08-06 00:00:00 +0000 - title: 'Bounding the Causal Impact of ML-assisted Decision-Making via Counterfactual Correctness' abstract: 'Predictive machine learning (ML) models are increasingly used to aid human decision-makers across various high-risk domains such as healthcare and criminal justice. There is a growing recognition of the need to evaluate the causal impact of deploying these systems on downstream outcomes, such as patient survival or crime recidivism. Randomized control trials (RCTs) can provide high-quality evidence on the impact of a deployed model, but they run into a challenge: it is often infeasible to run repeated trials when models are updated or retrained to improve predictive performance. In this work, we present a partial-identification approach to using prior {RCT} data to construct bounds on the causal effect of a new model. The core innovation in our approach is to leverage assumptions relating fine-grained predictive accuracy to downstream outcomes. We do so via two monotonicity assumptions: first, on individual-level ‘counterfactual correctness’ (all else being equal, a correct prediction leads to non-inferior outcomes); and second, on the relation between subgroup predictive performance and outcomes, interpretable as an assumption regarding trust in model outputs. We demonstrate our method with a simulation study, illustrating how incorporating this information can lead to more informative bounds compared to prior work.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26b/zhang26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Jonathan family: Zhang - given: Erik family: Skalnes - given: Jacob M. family: Chen - given: Michael family: Oberst editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8026-8070 id: zhang26b issued: date-parts: - 2026 - 8 - 6 firstpage: 8026 lastpage: 8070 published: 2026-08-06 00:00:00 +0000 - title: 'Interpretable Causal Discovery via Causal-Effect Constraints' abstract: 'Causal discovery aims to uncover the underlying causal relationships given data generated from a system. The goal, however, is not merely to predict causal edges given data, but also to be able to interpret and explain either observed or hypothesized phenomena, such as a particularly large causal effect. We consider this task of conditional causal discovery and cast it as a {Bayesian} inference problem, in which we target the posterior over causal graphs and parameters conditional on an event such as a causal-effect constraint. Unfortunately, this poses a computational challenge: existing approaches to {Bayesian} causal discovery struggle when the event has small posterior mass. To address this, we adapt rare-event estimation techniques to perform inference the joint graph-parameter space. Our method gradually drives a particle population toward the constrained region while maintaining samples that approximate the conditional posterior. Empirical evaluation on synthetic graphs validates the accuracy of our approach at small and large scales, and we show in a case study on the Sachs protein dataset how our method can be used to aid scientific exploration by providing pathway-level summaries.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26c.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26c/zhang26c.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26c.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Cixuan family: Zhang - given: Guy prefix: Van den family: Broeck - given: Benjie family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8071-8089 id: zhang26c issued: date-parts: - 2026 - 8 - 6 firstpage: 8071 lastpage: 8089 published: 2026-08-06 00:00:00 +0000 - title: 'FedSteer: Taming Extreme Gradient Staleness in Federated Learning with Corrective Projections and Caching' abstract: 'Federated learning (FL) is often subject to aggregation variance if clients do not consistently participate in training rounds. While reusing stale model updates from inactive clients is a common technique to reduce this variance, we find that with skewed client participation, the resulting update staleness can become severe enough to destabilize training. To remedy this, we propose FedSteer, a novel method that constructs a gradient subspace from a cache of recent client gradients to serve as a low-dimensional representation of the current optimization landscape. FedSteer projects an active client’s true gradient onto this subspace to find a set of optimal coordinates. For an inactive client, FedSteer reuses these coordinates with the now-evolved subspace drifted by other active clients. This process effectively “steers” outdated gradients toward the current global objective. This is complemented by a selective caching strategy that identifies a representative client subset to form the subspace, reducing server memory. Experiments demonstrate that FedSteer significantly outperforms baselines, preventing performance collapse in challenging scenarios while delivering accuracy gains of over 7% in others.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26d.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26d/zhang26d.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26d.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Haoran family: Zhang - given: Cainã Figueiredo family: Pereira - given: Marie family: Siew - given: Xutong family: Liu - given: Carlee family: Joe-Wong - given: Rachid family: El-Azouzi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8090-8114 id: zhang26d issued: date-parts: - 2026 - 8 - 6 firstpage: 8090 lastpage: 8114 published: 2026-08-06 00:00:00 +0000 - title: 'Not All Queries Need Deep Thought: CoFiCot for Adaptive Coarse-to-fine Stateful Refinement' abstract: 'Scaling test-time computation enhances {LLM} reasoning ability but faces a uniform computation paradox. Allocating identical resources leads to over-correction on simple tasks and insufficient refinement on complex ones. To address this, we propose {CoFiCot}, a coarse-to-fine adaptive framework that dynamically tailors inference strategies to problem difficulty. Specifically, we implement a multi-metric classifier that triages queries by synthesizing semantic entropy, consensus reliability, and predicted reasoning depth . This enables a differentiated refinement stage that applies efficient aggregation for simple queries while routing complex ones to a context-aware correction loop . We formalize correction as a stateful sequential propagation process , where each repair is strictly conditioned on the verified history of prior rectifications. By integrating Process Reward Models (PRMs) within this state-dependent trajectory, {CoFiCot} effectively bridges the gap between granular error localization and global logical coherence, preventing the context fragmentation typical of stateless refinement methods.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26e.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26e/zhang26e.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26e.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Dongxu family: Zhang - given: Hongqiang family: Lin - given: Yiding family: Sun - given: Pengyu family: Wang - given: Qirui family: Wang - given: Ning family: Yang - given: Jihua family: Zhu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8115-8129 id: zhang26e issued: date-parts: - 2026 - 8 - 6 firstpage: 8115 lastpage: 8129 published: 2026-08-06 00:00:00 +0000 - title: 'Instrumental and Proximal Causal Inference with Gaussian Processes' abstract: 'Instrumental variable (IV) and proximal causal learning (Proxy) methods are central frameworks for causal inference in the presence of unobserved confounding. Despite substantial methodological advances, existing approaches rarely provide reliable epistemic uncertainty (EU) quantification. We address this gap through a Deconditional {Gaussian} Process (GP) framework for uncertainty-aware causal learning. Our formulation recovers popular kernel estimators as the posterior mean, ensuring predictive precision, while the posterior variance yields principled and well-calibrated EU. Moreover, the probabilistic structure enables systematic model selection via marginal log-likelihood optimization. Empirical results demonstrate strong predictive performance alongside informative EU quantification, evaluated via empirical coverage frequencies and decision-aware accuracy–rejection curves. Together, our approach provides a unified, practical solution for causal inference under unobserved confounding with reliable uncertainty.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26f.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26f/zhang26f.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26f.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuqi family: Zhang - given: Krikamol family: Muandet - given: Dino family: Sejdinovic - given: Edwin family: Fong - given: Siu Lun family: Chau editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8130-8165 id: zhang26f issued: date-parts: - 2026 - 8 - 6 firstpage: 8130 lastpage: 8165 published: 2026-08-06 00:00:00 +0000 - title: 'Gungnir: Exploiting Stylistic Features in Images for Backdoor Attacks on Diffusion Models' abstract: 'Diffusion Models (DMs) have achieved remarkable success in image generation, yet recent studies reveal their vulnerability to backdoor attacks, where adversaries manipulate outputs via covert triggers embedded in inputs. Existing defenses, such as backdoor detection and trigger inversion, are largely effective because prior attacks rely on limited input spaces and low-dimensional triggers that are visually conspicuous or easily captured by neural detectors. To broaden the threat landscape, we propose Gungnir, a novel backdoor attack that activates malicious behaviors through style-based triggers embedded in input images. Unlike explicit visual patches or textual cues, stylistic features serve as stealthy, high-level triggers. We introduce Reconstructing-Adversarial Noise (RAN) and Short-Term Timesteps-Retention (STTR) to preserve trigger-consistent diffusion dynamics in image-to-image tasks. The resulting trigger-embedded samples are perceptually indistinguishable from clean images, evading both manual and automated detection. Extensive experiments show that Gungnir bypasses state-of-the-art defenses with an extremely low backdoor detection rate (BDR) and remains effective under fine-tuning-based purification, revealing previously underexplored vulnerabilities in diffusion models.' volume: 337 URL: https://proceedings.mlr.press/v337/zhang26g.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhang26g/zhang26g.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhang26g.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Lei family: Zhang - given: Yu family: Pan - given: Bingrong family: Dai - given: Lin family: Wang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8166-8181 id: zhang26g issued: date-parts: - 2026 - 8 - 6 firstpage: 8166 lastpage: 8181 published: 2026-08-06 00:00:00 +0000 - title: 'Efficient Decentralized Learning of Generalized Quantal Response Equilibrium' abstract: 'We study a solution concept for bounded rational agents in finite normal-form general-sum games called Generalized Quantal Response Equilibrium (GQRE) which generalizes a Quantal Response Equilibrium (McKelvey and Palfrey, 1995). In our setup, each player can individually maximize a smooth, regularized expected utility of the mixed profiles used, reflecting both bounded rationality that subsumes stochastic choice, and also individual choice of behaviors. After establishing existence under mild conditions, we present a computationally efficient no-regret decentralized learning algorithm that uses a smoothened version of the Frank–Wolfe algorithm coupled with a computationally efficient projection step. Our algorithm uses noisy gradient estimates via bandit-feedback from a simulation oracle that reports on repeated plays of the game. We analyze finite-time convergence properties of our algorithm under assumptions that ensure uniqueness of equilibrium, using a novel class of gap functions that generalize the {Nash} gap function. We end by demonstrating the effectiveness of our method on a set of complex general-sum games such as high-rank two-player games, large action two-player games, and known examples of difficult multi-player games.' volume: 337 URL: https://proceedings.mlr.press/v337/zhao26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhao26a/zhao26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhao26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zehao family: Zhao - given: Apurv family: Shukla - given: Rahul family: Jain - given: Vijay G family: Subramanian editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8182-8208 id: zhao26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8182 lastpage: 8208 published: 2026-08-06 00:00:00 +0000 - title: 'SeSE: Black-Box Uncertainty Quantification for Large Language Models Based on Structural Information Theory' abstract: 'Reliable uncertainty quantification (UQ) is essential for deploying large language models ({LLMs}) in safety-critical scenarios, as it enables them to abstain from responding when uncertain, thereby avoiding hallucinations, i.e., plausible yet factually incorrect responses. However, while current semantic UQ methods have achieved state-of-the-art performance, they inherently overlook latent semantic structural information that could enable more precise uncertainty estimates. In this paper, we propose Semantic Structural Entropy ({SeSE}), a principled black-box UQ framework applicable to both open- and closed-source {LLMs}. To reveal the intrinsic structure of the {LLM} semantic space, {SeSE} constructs its hierarchical abstraction based on the principle of structural entropy minimization. The structural entropy of the resulting optimal hierarchical abstraction thus quantifies the inherent uncertainty within the semantic space after optimal compression. Additionally, unlike existing methods that primarily focus on simple short-form generation, we extend {SeSE} to provide interpretable and granular uncertainty estimation for long-form outputs. We theoretically prove that {SeSE} generalizes semantic entropy, the gold standard for UQ in {LLMs}, and empirically demonstrate its superior performance over baselines across 24 model-dataset combinations.' volume: 337 URL: https://proceedings.mlr.press/v337/zhao26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhao26b/zhao26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhao26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Xingtao family: Zhao - given: Hao family: Peng - given: Dingli family: Su - given: Xianghua family: Zeng - given: Chunyang family: Liu - given: Jinzhi family: Liao - given: Philip S. family: Yu editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8209-8237 id: zhao26b issued: date-parts: - 2026 - 8 - 6 firstpage: 8209 lastpage: 8237 published: 2026-08-06 00:00:00 +0000 - title: 'Self-Supervised Uncertainty Estimation For Super-Resolution of Satellite Images' abstract: 'Super-resolution (SR) of satellite imagery is challenging due to the lack of paired low-/high-resolution data. Recent self-supervised SR methods overcome this limitation by exploiting the temporal redundancy in burst observations, but they lack a mechanism to quantify uncertainty in the reconstruction. In this work, we introduce a novel self-supervised loss that allows to estimate uncertainty in image super-resolution without ever accessing the ground-truth high-resolution data. We adopt a decision-theoretic perspective and show that minimizing the corresponding {Bayesian} risk yields the posterior mean and variance as optimal estimators. We validate our approach on a synthetic dataset with both white and signal dependent noise and demonstrate that it produces calibrated uncertainty estimates comparable to supervised methods. We further apply our method on real SkySat satellite data and validate its performance through an unsupervised coverage test. Our work bridges self-supervised restoration with uncertainty quantification, making a practical framework for uncertainty-aware image reconstruction.' volume: 337 URL: https://proceedings.mlr.press/v337/zheng26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zheng26a/zheng26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zheng26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Zhe family: Zheng - given: Valéry family: Dewil - given: Pablo family: Arias editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8238-8252 id: zheng26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8238 lastpage: 8252 published: 2026-08-06 00:00:00 +0000 - title: 'Uncertainty Quantification of Click and Conversion Estimates for the Autobidding' abstract: 'Modern e-commerce platforms employ various auction mechanisms to allocate paid slots for a given item. To scale this approach to the millions of auctions, the platforms suggest promotion tools based on the autobidding algorithms. These algorithms typically depend on the Click-Through-Rate (CTR) and Conversion-Rate (CVR) estimates provided by a pre-trained machine learning model. However, the predictions of such models are uncertain and can significantly affect the performance of the autobidding algorithm. To address this issue, we propose the $\texttt{DenoiseBid}$ method, which corrects the generated CTRs and CVRs to make the resulting bids more efficient in auctions. The underlying idea of our method is to employ a {Bayesian} approach and replace noisy CTR or CVR estimates with those from recovered distributions. To demonstrate the performance of the proposed approach, we perform extensive experiments on the synthetic, iPinYou, and BAT datasets. To evaluate the robustness of our approach to the noise scale, we use synthetic noise and noise estimated from the predictions of the pre-trained machine learning model.' volume: 337 URL: https://proceedings.mlr.press/v337/zhigalskii26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhigalskii26a/zhigalskii26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhigalskii26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Ivan family: Zhigalskii - given: Andrey family: Pudovikov - given: Aleksandr family: Katrutsa - given: Egor family: Samosvat editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8253-8269 id: zhigalskii26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8253 lastpage: 8269 published: 2026-08-06 00:00:00 +0000 - title: 'Bandwidth Selection in Kernel Density Estimation for Model Calibration' abstract: 'As deep learning models are increasingly deployed in high-stakes applications, providing well-calibrated uncertainty estimates has become as critical as achieving high predictive accuracy. While Kernel Density Estimation (KDE) has emerged as a smooth and continuous alternative to traditional binning for quantifying miscalibration, its reliability is heavily dependent on the choice of the kernel bandwidth. Standard selection techniques, such as Maximum Likelihood Estimation (MLE), often fail to produce optimal bandwidths for calibration tasks. In this work, we introduce Risk Alignment (RA), a novel optimization framework that determines the optimal bandwidth by aligning KDE-reconstructed risk with empirical risk. We theoretically demonstrate that this alignment minimizes calibration estimation bias across the data distribution, establishing a principled bandwidth selection criterion applicable to various metrics, including the challenging case of canonical calibration error. Extensive experiments across multiple architectures and datasets show that RA consistently outperforms standard bandwidth selection methods, yielding more reliable calibration assessments.' volume: 337 URL: https://proceedings.mlr.press/v337/zhou26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhou26a/zhou26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhou26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Han family: Zhou - given: Teodora family: Popordanoska - given: Matthew B. family: Blaschko editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8270-8291 id: zhou26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8270 lastpage: 8291 published: 2026-08-06 00:00:00 +0000 - title: 'Unified Confidence Adjustment for Robust Cross-Modal Retrieval under Test-Time Distribution Shifts' abstract: 'Cross-modal retrieval models often suffer substantial performance degradation under test-time distribution shifts. Existing test-time adaptation methods primarily based on entropy minimization tend to sharpen the similarity distribution. However, retrieval relies on feature similarities to rank candidates, and the similarity gaps between nearby-ranked candidates are often small. Over-sharpening the similarity gap between the candidates can distort the semantic similarity structure, leading to miscalibrated updates and unstable retrieval. To address this issue, we propose a novel *Unified Confidence Adjustment* framework that explicitly accounts for semantic similarity within the candidate set. Specifically, we propose the *Semantic Proximity Margin* as a confidence prior. Building on this margin, we develop a *Confidence State Identification* mechanism and a *Unified Confidence Adjustment* strategy for adaptive confidence calibration. Extensive experiments on four benchmarks under both zero-shot transfer and natural corruption settings show that our proposal consistently outperforms state-of-the-art test-time adaptation methods with minimal computational overhead, underscoring the effectiveness of confidence-aware regularization for robust cross-modal retrieval.' volume: 337 URL: https://proceedings.mlr.press/v337/zhou26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhou26b/zhou26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhou26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Rui family: Zhou - given: Yawen family: Hao - given: Hao family: Zuo - given: Xinhang family: Wan - given: Cheng family: Zhu - given: Yun family: Zhou editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8292-8311 id: zhou26b issued: date-parts: - 2026 - 8 - 6 firstpage: 8292 lastpage: 8311 published: 2026-08-06 00:00:00 +0000 - title: 'Approximating Probabilistic Inference in Statistical $\mathcalEL$ with Knowledge Graph Embeddings' abstract: 'In domains where statistical data is collected across hierarchically organized categories, drawing valid conclusions requires reasoning jointly about proportions and the structure of the domain. Statistical $\mathcal{EL}$ ($\mathcal{SEL}$) formalizes this kind of reasoning, but exact inference is \textsc{ExpTime}-hard and no implementation exists. We show how knowledge graph embeddings can approximate $\mathcal{SEL}$ inference efficiently. We prove analytical runtime and soundness guarantees, and empirically evaluate the runtime and approximation quality of our approach.' volume: 337 URL: https://proceedings.mlr.press/v337/zhu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zhu26a/zhu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zhu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Yuqicheng family: Zhu - given: Nico family: Potyka - given: Bo family: Xiong - given: Trung-Kien family: Tran - given: Mojtaba family: Nayyeri - given: Evgeny family: Kharlamov - given: Steffen family: Staab editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8312-8329 id: zhu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8312 lastpage: 8329 published: 2026-08-06 00:00:00 +0000 - title: 'Revisiting TD Target Aggregation under Uncertainty in Q-Learning' abstract: 'Deep Q-Networks (DQNs) learn value functions through bootstrapped temporal-difference updates, where future returns are approximated using a greedy maximization over next-state action values. While effective, this aggregation rule is inherently sensitive to estimation noise: when Q-values are uncertain, the maximization operator deterministically favors the largest estimate, regardless of its reliability, leading to amplified errors through bootstrapping. In this work, we propose the **S**uccessor Rollout **A**ggregation **D**eep **Q**-Network (SADQ), a simple modification to Q-learning that regularizes how the {TD} target is formed. SADQ uses one-step rollout predictions from a learned dynamics model to guide the comparison among candidate next-state actions, introducing additional structure into the aggregation step without altering the underlying learning framework. The resulting mixed {Bellman} update attenuates unreliable maxima while preserving the standard fixed point under diminishing model error. We provide theoretical analysis showing that SADQ reduces bootstrap-induced overestimation in a pointwise manner. Empirically, SADQ consistently improves training stability across classical control tasks, real-world vector-based environments, and Atari benchmarks when compared to strong DQN variants.' volume: 337 URL: https://proceedings.mlr.press/v337/zu26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zu26a/zu26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zu26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Lipeng family: Zu - given: Xiaonan family: Zhang editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8330-8348 id: zu26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8330 lastpage: 8348 published: 2026-08-06 00:00:00 +0000 - title: 'Towards Identifiability of Interventional Stochastic Differential Equations' abstract: 'We study identifiability of stochastic differential equations (SDE) under multiple interventions. Our results give the first provable bounds for unique recovery of SDE parameters given samples from their stationary distributions. We give tight bounds on the number of necessary interventions for linear SDEs, and upper bounds for nonlinear SDEs in the small noise regime. We experimentally validate the recovery of true parameters in synthetic data, and motivated by our theoretical results, demonstrate the advantage of parameterizations with learnable activation functions in application to gene regulatory dynamics.' volume: 337 URL: https://proceedings.mlr.press/v337/zweig26a.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zweig26a/zweig26a.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zweig26a.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Aaron family: Zweig - given: Zaikang family: Lin - given: Elham family: Azizi - given: David A. family: Knowles editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8349-8374 id: zweig26a issued: date-parts: - 2026 - 8 - 6 firstpage: 8349 lastpage: 8374 published: 2026-08-06 00:00:00 +0000 - title: 'Learning Lineage-guided Geodesics with Finsler Geometry' abstract: 'Trajectory inference investigates how to interpolate paths between observed timepoints of dynamical systems, such as temporally resolved population distributions, with the goal of inferring trajectories at unseen times and better understanding system dynamics. Previous work has focused on continuous geometric priors, utilizing data-dependent spatial features to define a Riemannian metric. In many applications, there exists discrete, directed prior knowledge over admissible transitions (e.g. lineage trees in developmental biology). We introduce a {Finsler} metric that combines geometry with classification and incorporate both types of priors in trajectory inference, yielding improved performance on interpolation tasks in synthetic and real-world data.' volume: 337 URL: https://proceedings.mlr.press/v337/zweig26b.html PDF: https://raw.githubusercontent.com/mlresearch/v337/main/assets/zweig26b/zweig26b.pdf edit: https://github.com/mlresearch//v337/edit/gh-pages/_posts/2026-08-06-zweig26b.md series: 'Proceedings of Machine Learning Research' container-title: 'Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence' publisher: 'PMLR' author: - given: Aaron family: Zweig - given: Mingxuan family: Zhang - given: David A. family: Knowles - given: Elham family: Azizi editor: - given: Emilija family: Perković - given: Daniel family: Malinsky page: 8375-8386 id: zweig26b issued: date-parts: - 2026 - 8 - 6 firstpage: 8375 lastpage: 8386 published: 2026-08-06 00:00:00 +0000