Probabilistic Edge Modulation for High-Dimensional Causal Discovery

Seyong Hwang, Kyoungjae Lee, Sunmin Oh, Gunwoong Park
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:2314-2335, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-hwang26a, title = {Probabilistic Edge Modulation for High-Dimensional Causal Discovery}, author = {Hwang, Seyong and Lee, Kyoungjae and Oh, Sunmin and Park, Gunwoong}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {2314--2335}, 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/hwang26a/hwang26a.pdf}, url = {https://proceedings.mlr.press/v337/hwang26a.html}, 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.} }
Endnote
%0 Conference Paper %T Probabilistic Edge Modulation for High-Dimensional Causal Discovery %A Seyong Hwang %A Kyoungjae Lee %A Sunmin Oh %A Gunwoong Park %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-hwang26a %I PMLR %P 2314--2335 %U https://proceedings.mlr.press/v337/hwang26a.html %V 337 %X 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.
APA
Hwang, S., Lee, K., Oh, S. & Park, G.. (2026). Probabilistic Edge Modulation for High-Dimensional Causal Discovery. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:2314-2335 Available from https://proceedings.mlr.press/v337/hwang26a.html.

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