PCU: Perturbation-Calibrated Uncertainty for Unsupervised Anomaly Detection

Mebarka Allaoui, Rachid Hedjam, Mohand Saïd Allili, Guoqiang Zhong
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:39-61, 2026.

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}}.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-allaoui26a, title = {{PCU}: Perturbation-Calibrated Uncertainty for Unsupervised Anomaly Detection}, author = {Allaoui, Mebarka and Hedjam, Rachid and Allili, Mohand Sa\"{i}d and Zhong, Guoqiang}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {39--61}, year = {2026}, editor = {Perković, Emilija and Malinsky, Daniel}, volume = {337}, series = {Proceedings of Machine Learning Research}, month = {17--21 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v337/main/assets/allaoui26a/allaoui26a.pdf}, url = {https://proceedings.mlr.press/v337/allaoui26a.html}, 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}}.} }
Endnote
%0 Conference Paper %T PCU: Perturbation-Calibrated Uncertainty for Unsupervised Anomaly Detection %A Mebarka Allaoui %A Rachid Hedjam %A Mohand Saïd Allili %A Guoqiang Zhong %B Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2026 %E Emilija Perković %E Daniel Malinsky %F pmlr-v337-allaoui26a %I PMLR %P 39--61 %U https://proceedings.mlr.press/v337/allaoui26a.html %V 337 %X 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}}.
APA
Allaoui, M., Hedjam, R., Allili, M.S. & Zhong, G.. (2026). PCU: Perturbation-Calibrated Uncertainty for Unsupervised Anomaly Detection. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:39-61 Available from https://proceedings.mlr.press/v337/allaoui26a.html.

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