Quantification of Credal Uncertainty: A Distance-Based Approach

Xabier Gonzalez-Garcia, Siu Lun Chau, Julian Rodemann, Michele Caprio, Krikamol Muandet, Humberto Bustince, Sebastien Destercke, Eyke Hüllermeier, Yusuf Sale
Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, PMLR 337:1725-1747, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v337-gonzalez-garcia26a, title = {Quantification of Credal Uncertainty: A Distance-Based Approach}, author = {Gonzalez-Garcia, Xabier and Chau, Siu Lun and Rodemann, Julian and Caprio, Michele and Muandet, Krikamol and Bustince, Humberto and Destercke, Sebastien and H\"{u}llermeier, Eyke and Sale, Yusuf}, booktitle = {Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence}, pages = {1725--1747}, 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/gonzalez-garcia26a/gonzalez-garcia26a.pdf}, url = {https://proceedings.mlr.press/v337/gonzalez-garcia26a.html}, 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.} }
Endnote
%0 Conference Paper %T Quantification of Credal Uncertainty: A Distance-Based Approach %A Xabier Gonzalez-Garcia %A Siu Lun Chau %A Julian Rodemann %A Michele Caprio %A Krikamol Muandet %A Humberto Bustince %A Sebastien Destercke %A Eyke Hüllermeier %A Yusuf Sale %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-gonzalez-garcia26a %I PMLR %P 1725--1747 %U https://proceedings.mlr.press/v337/gonzalez-garcia26a.html %V 337 %X 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.
APA
Gonzalez-Garcia, X., Chau, S.L., Rodemann, J., Caprio, M., Muandet, K., Bustince, H., Destercke, S., Hüllermeier, E. & Sale, Y.. (2026). Quantification of Credal Uncertainty: A Distance-Based Approach. Proceedings of the 42nd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 337:1725-1747 Available from https://proceedings.mlr.press/v337/gonzalez-garcia26a.html.

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