Structured Credal Learning

Varun Venkatesh, Eyke Hüllermeier, Bernd Bischl, Mina Rezaei
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:6917-6952, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-venkatesh26a, title = {Structured Credal Learning}, author = {Venkatesh, Varun and H\"{u}llermeier, Eyke and Bischl, Bernd and Rezaei, Mina}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {6917--6952}, 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/venkatesh26a/venkatesh26a.pdf}, url = {https://proceedings.mlr.press/v337/venkatesh26a.html}, 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.} }
Endnote
%0 Conference Paper %T Structured Credal Learning %A Varun Venkatesh %A Eyke Hüllermeier %A Bernd Bischl %A Mina Rezaei %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-venkatesh26a %I PMLR %P 6917--6952 %U https://proceedings.mlr.press/v337/venkatesh26a.html %V 337 %X 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.
APA
Venkatesh, V., Hüllermeier, E., Bischl, B. & Rezaei, M.. (2026). Structured Credal Learning. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:6917-6952 Available from https://proceedings.mlr.press/v337/venkatesh26a.html.

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