Quantification of Credal Uncertainty: A Distance-Based Approach

Computer Science > Artificial Intelligence [Submitted on 28 Mar 2026] Quantification of Credal Uncertainty: A Distance-Based Approach Xabier Gonzalez-Garcia, Siu Lun Chau, Julian Rodemann, Michele Caprio, Krikamol Muandet, Humberto Bustince, Sébastien Destercke, Eyke Hüllermeier, Yusuf Sale 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 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. Subjects: Artificial Intelligence (cs.AI); Machine Learning (stat.ML) Cite as: arXiv:2603.27270 [cs.AI]   (or arXiv:2603.27270v1 [cs.AI] for this version)   https://doi.org/10.48550/arXiv.2603.27270 Focus to learn more Submission history From: Xabier Gonzalez-Garcia [view email] [v1] Sat, 28 Mar 2026 13:50:48 UTC (3,235 KB) Access Paper: view license Current browse context: cs.AI < prev   |   next > new | recent | 2026-03 Change to browse by: cs stat stat.ML References & Citations NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)