Quantification of Credal Uncertainty: A Distance-Based Approach
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arXiv
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| Main Authors: | , , , , , , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866915897235472384 |
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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 |