mlsanityData to 7 Oct 2026

Quantification of Credal Uncertainty: A Distance-Based Approach

arXiv 2603.27270 ↗First posted 28 Mar 2026cs.AI stat.MLcited by 2

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Abstract (arXiv)

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.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 24 of its 71 references that are in the map. First posted on arXiv 28 Mar 2026.

Builds on

24 of 71 references.

References · 24

  1. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,416
  2. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  3. 2021Convex optimizationcited by 2,479
  4. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  5. 2018Evidential Deep Learning to Quantify Classification Uncertaintycited by 728
  6. 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
  7. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 360
  8. 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 124
  9. 2023Credal Bayesian Deep Learningcited by 45
  10. 2023Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?cited by 40
  11. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  12. 2024Credal Learning Theorycited by 30
12 more
  1. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  2. 2024Label-wise Aleatoric and Epistemic Uncertainty Quantificationcited by 22
  3. 2024Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rulescited by 21
  4. 2024Credal Two-Sample Tests of Epistemic Uncertaintycited by 16
  5. 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classificationcited by 13
  6. 2025Integral Imprecise Probability Metricscited by 11
  7. 2025Credal Prediction based on Relative Likelihoodcited by 8
  8. 2025Conformal Prediction Regions are Imprecise Highest Density Regionscited by 7
  9. 2025Uncertainty Quantification for Machine Learning: One Size Does Not Fit Allcited by 4
  10. 2026Quantifying Epistemic Predictive Uncertainty in Conformal Predictioncited by 4
  11. 2024A Rate-Distortion View of Uncertainty Quantificationcited by 3
  12. 2013Calculating Uncertainty Intervals From Conditional Convex Sets of Probabilitiescited by 2

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2026: 2.

2 papers.

  1. 2026Credal Large Language Models for Semantic Commitment under Uncertaintycited by 2
  2. 2026On the QUEST for Uncertainty Quantification via Highest Density Regionscited by 0