mlsanityData to 14 Oct 2026

Credal Learning Theory

arXiv 2402.00957 ↗First posted 1 Feb 2024cs.LG cs.AI stat.MLcited by 31

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Abstract (arXiv)

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution. In actual deployment, however, the data distribution may (and often does) vary, causing domain adaptation/generalization issues. In this paper we lay the foundations for a `credal' theory of learning, using convex sets of probabilities (credal sets) to model the variability in the data-generating distribution. Such credal sets, we argue, may be inferred from a finite sample of training sets. Bounds are derived for the case of finite hypotheses spaces (both assuming realizability or not), as well as infinite model spaces, which directly generalize classical results.

Key facts. Cited by 31 papers in the map (data through 14 Oct 2026). Builds on 32 of its 80 references that are in the map. First posted on arXiv 1 Feb 2024.

Builds on

32 of 80 references.

References · 32

  1. 2020WILDS: A Benchmark of in-the-Wild Distribution Shiftscited by 1,375
  2. 2018Averaging Weights Leads to Wider Optima and Better Generalizationcited by 1,209
  3. 2020In Search of Lost Domain Generalizationcited by 1,054
  4. 2021Generalizing to Unseen Domains: A Survey on Domain Generalizationcited by 766
  5. 2021Domain Generalization: A Surveycited by 764
  6. 2018Evidential Deep Learning to Quantify Classification Uncertaintycited by 732
  7. 2013Domain Generalization via Invariant Feature Representationcited by 623
  8. 2021SWAD: Domain Generalization by Seeking Flat Minimacited by 434
  9. 2019Generalizing to unseen domains via distribution matchingcited by 110
  10. 2020A survey on domain adaptation theory: learning bounds and theoretical guaranteescited by 109
  11. 2021Towards a Theoretical Framework of Out-of-Distribution Generalizationcited by 94
  12. 2019Domain Generalization via Multidomain Discriminant Analysiscited by 69
20 more
  1. 2023Credal Bayesian Deep Learningcited by 45
  2. 2023Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?cited by 40
  3. 2015Optimal Testing for Properties of Distributionscited by 36
  4. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  5. 2023Continual Self-supervised Learning: Towards Universal Multi-modal Medical Data Representation Learningcited by 34
  6. 2021An Online Learning Approach to Interpolation and Extrapolation in Domain Generalizationcited by 30
  7. 2018Robust Hypothesis Testing Using Wasserstein Uncertainty Setscited by 28
  8. 2019A Generalization Error Bound for Multi-class Domain Generalizationcited by 26
  9. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  10. 2022Integral Probability Metrics PAC-Bayes Boundscited by 19
  11. 2021Credal Self-Supervised Learningcited by 15
  12. 2022Domain Generalization -- A Causal Perspectivecited by 14
  13. 2023A Novel Bayes' Theorem for Upper Probabilitiescited by 13
  14. 2022Understanding Robust Learning through the Lens of Representation Similaritiescited by 12
  15. 2023Just a Glimpse: Rethinking Temporal Information for Video Continual Learningcited by 10
  16. 2017Judicious Judgment Meets Unsettling Updating: Dilation, Sure Loss, and Simpson's Paradoxcited by 8
  17. 2022On the Calibration of Probabilistic Classifier Setscited by 8
  18. 2021Valid inferential models for prediction in supervised learning problemscited by 7
  19. 2022Sketching Algorithms and Lower Bounds for Ridge Regressioncited by 4
  20. 2013On the Complexity of Strong and Epistemic Credal Networkscited by 1

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 15; 2026: 11.

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  1. 2024Conformalized Credal Regions for Classification with Ambiguous Ground Truthcited by 19
  2. 2025A Unified Evaluation Framework for Epistemic Predictionscited by 10
  3. 2025Position: Epistemic uncertainty estimation methods are fundamentally incompletecited by 9
  4. 2025Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'cited by 8
  5. 2025Conformal Prediction Regions are Imprecise Highest Density Regionscited by 7
  6. 2025Random-Set Large Language Modelscited by 7
  7. 2025Truthful Elicitation of Imprecise Forecastscited by 6
  8. 2024Generalising realisability in statistical learning theory under epistemic uncertaintycited by 5
  9. 2025Epistemic Wrapping for Uncertainty Quantificationcited by 5
  10. 2025Generalization Bounds and Stopping Rules for Learning with Self-Selected Datacited by 5
  11. 2026Beyond Prediction-Set Size: Quantifying Conformal Uncertainty through Credal Geometrycited by 4
  12. 2025Optimal Conformal Prediction under Epistemic Uncertaintycited by 3
19 more
  1. 2026Random-Set Graph Neural Networkscited by 3
  2. 2024Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantificationcited by 2
  3. 2025Credal Graph Neural Networkscited by 2
  4. 2025Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluationcited by 2
  5. 2026Quantification of Credal Uncertainty: A Distance-Based Approachcited by 2
  6. 2026Credal Large Language Models for Semantic Commitment under Uncertaintycited by 2
  7. 2025Reliable Classification with Conformal Learning and Interval-Type 2 Fuzzy Setscited by 1
  8. 2025Epistemic Errors of Imperfect Multitask Learners When Distributions Shiftcited by 1
  9. 2025When Do Credal Sets Stabilize? Fixed-Point Theorems for Credal Set Updatescited by 1
  10. 2025Maxitive Donsker-Varadhan Formulation for Possibilistic Variational Inferencecited by 1
  11. 2026Efficient Credal Prediction through Decalibrationcited by 1
  12. 2026Structured Credal Learningcited by 1
  13. 2026A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classificationcited by 1
  14. 2026A formal definition and meta-model for a machine theory of mindcited by 1
  15. 2024SSP-RACL: Classification of Noisy Fundus Images with Self-Supervised Pretraining and Robust Adaptive Credal Losscited by 0
  16. 2024Optimal Transport for ε-Contaminated Credal Sets: To the Memory of Sayan Mukherjeecited by 0
  17. 2026Upper Entropy for 2-Monotone Lower Probabilitiescited by 0
  18. 2026The Physical Cutoff Does Not Restore Homogenization: Phase-Dependent Burning in the Strain G-Equationcited by 0
  19. 2026XU-RS: Explaining Credal Width in Random-Set Language Modelscited by 0