mlsanityData to 7 Oct 2026

Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?

arXiv 2306.09586 ↗First posted 16 Jun 2023cs.LG cs.AI stat.MLcited by 40

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Abstract (arXiv)

Adequate uncertainty representation and quantification have become imperative in various scientific disciplines, especially in machine learning and artificial intelligence. As an alternative to representing uncertainty via one single probability measure, we consider credal sets (convex sets of probability measures). The geometric representation of credal sets as d-dimensional polytopes implies a geometric intuition about (epistemic) uncertainty. In this paper, we show that the volume of the geometric representation of a credal set is a meaningful measure of epistemic uncertainty in the case of binary classification, but less so for multi-class classification. Our theoretical findings highlight the crucial role of specifying and employing uncertainty measures in machine learning in an appropriate way, and for being aware of possible pitfalls.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). Builds on 10 of its 53 references that are in the map. First posted on arXiv 16 Jun 2023.

Builds on

10 of 53 references.

References · 10

  1. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  2. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  3. 2018Understanding Measures of Uncertainty for Adversarial Example Detectioncited by 177
  4. 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 124
  5. 2022Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisationcited by 65
  6. 2016On the Safety of Machine Learning: Cyber-Physical Systems, Decision Sciences, and Data Productscited by 52
  7. 2022On Uncertainty, Tempering, and Data Augmentation in Bayesian Classificationcited by 46
  8. 2023Credal Bayesian Deep Learningcited by 45
  9. 2020Aleatoric and Epistemic Uncertainty with Random Forestscited by 42
  10. 2016Engineering Safety in Machine Learningcited by 24

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 4; 2024: 14; 2025: 12; 2026: 10.

40 papers.

Sort:

  1. 2024Rethinking Aleatoric and Epistemic Uncertaintycited by 40
  2. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  3. 2024Credal Learning Theorycited by 30
  4. 2023Introducing an Improved Information-Theoretic Measure of Predictive Uncertaintycited by 28
  5. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  6. 2024Label-wise Aleatoric and Epistemic Uncertainty Quantificationcited by 22
  7. 2024Conformalized Credal Set Predictorscited by 21
  8. 2023Random-Set Neural Networks (RS-NN)cited by 19
  9. 2024Conformalized Credal Regions for Classification with Ambiguous Ground Truthcited by 19
  10. 2024On Information-Theoretic Measures of Predictive Uncertaintycited by 16
  11. 2023A Novel Bayes' Theorem for Upper Probabilitiescited by 13
  12. 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classificationcited by 13
28 more
  1. 2025Integral Imprecise Probability Metricscited by 11
  2. 2025An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regressioncited by 9
  3. 2024Provable Uncertainty Decomposition via Higher-Order Calibrationcited by 8
  4. 2025Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'cited by 8
  5. 2025Credal and Interval Deep Evidential Classificationscited by 8
  6. 2025Conformal Prediction Regions are Imprecise Highest Density Regionscited by 7
  7. 2025A calibration test for evaluating set-based epistemic uncertainty representationscited by 7
  8. 2025Random-Set Large Language Modelscited by 7
  9. 2025Truthful Elicitation of Imprecise Forecastscited by 6
  10. 2026Learning Credal Ensembles via Distributionally Robust Optimizationcited by 6
  11. 2024Generalising realisability in statistical learning theory under epistemic uncertaintycited by 5
  12. 2025Epistemic Wrapping for Uncertainty Quantificationcited by 5
  13. 2026Quantifying Epistemic Predictive Uncertainty in Conformal Predictioncited by 4
  14. 2024Partial-Label Learning with a Reject Optioncited by 3
  15. 2026Random-Set Graph Neural Networkscited by 3
  16. 2024Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantificationcited by 2
  17. 2025Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluationcited by 2
  18. 2026Quantification of Credal Uncertainty: A Distance-Based Approachcited by 2
  19. 2024Conformal Predictions for Probabilistically Robust Scalable Machine Learning Classificationcited by 1
  20. 2025Robust Partial-Label Learning by Leveraging Class Activation Valuescited by 1
  21. 2025Reliable Classification with Conformal Learning and Interval-Type 2 Fuzzy Setscited by 1
  22. 2026A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classificationcited by 1
  23. 2024Optimal Transport for ε-Contaminated Credal Sets: To the Memory of Sayan Mukherjeecited by 0
  24. 2026Structurally Separated Uncertainty in Supervised Latent Variable Modelscited by 0
  25. 2026Efficient Credal Prediction through Decalibrationcited by 0
  26. 2026Credal Concept Bottleneck Models for Epistemic-Aleatoric Uncertainty Decompositioncited by 0
  27. 2026On the QUEST for Uncertainty Quantification via Highest Density Regionscited by 0
  28. 2026Uncertainty quantification for trustworthy deep learning: Methods and measurescited by 0