Quantification of Credal Uncertainty: A Distance-Based Approach

Fuente: arXiv
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Main Authors: Gonzalez-Garcia, Xabier, Chau, Siu Lun, Rodemann, Julian, Caprio, Michele, Muandet, Krikamol, Bustince, Humberto, Destercke, Sébastien, Hüllermeier, Eyke, Sale, Yusuf
Format: Preprint
Published: 2026
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author Gonzalez-Garcia, Xabier
Chau, Siu Lun
Rodemann, Julian
Caprio, Michele
Muandet, Krikamol
Bustince, Humberto
Destercke, Sébastien
Hüllermeier, Eyke
Sale, Yusuf
author_facet Gonzalez-Garcia, Xabier
Chau, Siu Lun
Rodemann, Julian
Caprio, Michele
Muandet, Krikamol
Bustince, Humberto
Destercke, Sébastien
Hüllermeier, Eyke
Sale, Yusuf
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2603_27270
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Quantification of Credal Uncertainty: A Distance-Based Approach
Gonzalez-Garcia, Xabier
Chau, Siu Lun
Rodemann, Julian
Caprio, Michele
Muandet, Krikamol
Bustince, Humberto
Destercke, Sébastien
Hüllermeier, Eyke
Sale, Yusuf
Artificial Intelligence
Machine Learning
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.
title Quantification of Credal Uncertainty: A Distance-Based Approach
topic Artificial Intelligence
Machine Learning
url https://arxiv.org/abs/2603.27270