mlsanityData to 7 Oct 2026

Credal Bayesian Deep Learning

arXiv 2302.09656 ↗First posted 19 Feb 2023cs.LG stat.MLcited by 45

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Abstract (arXiv)

Uncertainty quantification and robustness to distribution shifts are important goals in machine learning and artificial intelligence. Although Bayesian Neural Networks (BNNs) allow for uncertainty in the predictions to be assessed, different sources of predictive uncertainty cannot be distinguished properly. We present Credal Bayesian Deep Learning (CBDL). Heuristically, CBDL allows to train an (uncountably) infinite ensemble of BNNs, using only finitely many elements. This is possible thanks to prior and likelihood finitely generated credal sets (FGCSs), a concept from the imprecise probability literature. Intuitively, convex combinations of a finite collection of prior-likelihood pairs are able to represent infinitely many such pairs. After training, CBDL outputs a set of posteriors on the parameters of the neural network. At inference time, such posterior set is used to derive a set of predictive distributions that is in turn utilized to distinguish between (predictive) aleatoric and epistemic uncertainties, and to quantify them. The predictive set also produces either (i) a collection of outputs enjoying desirable probabilistic guarantees, or (ii) the single output that is deemed the best, that is, the one having the highest predictive lower probability -- another imprecise-probabilistic concept. CBDL is more robust than single BNNs to prior and likelihood misspecification, and to distribution shift. We show that CBDL is better at quantifying and disentangling different types of (predictive) uncertainties than single BNNs and ensemble of BNNs. In addition, we apply CBDL to two case studies to demonstrate its downstream tasks capabilities: one, for motion prediction in autonomous driving scenarios, and two, to model blood glucose and insulin dynamics for artificial pancreas control. We show that CBDL performs better when compared to an ensemble of BNNs baseline.

Key facts. Cited by 45 papers in the map (data through 7 Oct 2026). Builds on 23 of its 82 references that are in the map. First posted on arXiv 19 Feb 2023.

Builds on

23 of 82 references.

References · 23

  1. 2017On Calibration of Modern Neural Networkscited by 4,860
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  5. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
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  7. 2019Deep Evidential Regressioncited by 354
  8. 2022Conformal prediction beyond exchangeabilitycited by 348
  9. 2020Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Userscited by 336
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11 more
  1. 2020Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Countscited by 163
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2023: 5; 2024: 9; 2025: 18; 2026: 13.

45 papers.

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  1. 2023Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?cited by 40
  2. 2024Credal Learning Theorycited by 30
  3. 2024CreINNs: Credal-Set Interval Neural Networks for Uncertainty Estimation in Classification Taskscited by 26
  4. 2024Conformalized Credal Regions for Classification with Ambiguous Ground Truthcited by 19
  5. 2023A Novel Bayes' Theorem for Upper Probabilitiescited by 13
  6. 2024Credal Wrapper of Model Averaging for Uncertainty Estimation in Classificationcited by 13
  7. 2025Integral Imprecise Probability Metricscited by 11
  8. 2025A Unified Evaluation Framework for Epistemic Predictionscited by 10
  9. 2025Statistical Multicriteria Evaluation of LLM-Generated Textcited by 9
  10. 2024Uncertainty-based Offline Variational Bayesian Reinforcement Learning for Robustness under Diverse Data Corruptionscited by 8
  11. 2025Position: Epistemic uncertainty estimation methods are fundamentally incompletecited by 8
  12. 2025A calibration test for evaluating set-based epistemic uncertainty representationscited by 7
33 more
  1. 2026Learning Credal Ensembles via Distributionally Robust Optimizationcited by 6
  2. 2023IBCL: Zero-shot Model Generation under Stability-Plasticity Trade-offscited by 5
  3. 2024Generalising realisability in statistical learning theory under epistemic uncertaintycited by 5
  4. 2025Generalization Bounds and Stopping Rules for Learning with Self-Selected Datacited by 5
  5. 2025Off-Switching Not Guaranteedcited by 4
  6. 2026Quantifying Epistemic Predictive Uncertainty in Conformal Predictioncited by 4
  7. 2023Bayesian Generalization Error in Linear Neural Networks with Concept Bottleneck Structure and Multitask Formulationcited by 3
  8. 2025Optimal Conformal Prediction under Epistemic Uncertaintycited by 3
  9. 2025HybridFlow: Quantification of Aleatoric and Epistemic Uncertainty with a Single Hybrid Modelcited by 3
  10. 2024Towards Better Understanding of In-Context Learning Ability from In-Context Uncertainty Quantificationcited by 2
  11. 2025Distilling Calibration via Conformalized Credal Inferencecited by 2
  12. 2025Adaptive Conformal Guidance for Learning under Uncertaintycited by 2
  13. 2025Uncertainty Quantification for Physics-Informed Neural Networks with Extended Fiducial Inferencecited by 2
  14. 2025Unreliable Uncertainty Estimates with Monte Carlo Dropoutcited by 2
  15. 2025Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluationcited by 2
  16. 2026Bayesian Conformal Prediction as a Decision Risk Problemcited by 2
  17. 2026Quantification of Credal Uncertainty: A Distance-Based Approachcited by 2
  18. 2026Credal Large Language Models for Semantic Commitment under Uncertaintycited by 2
  19. 2023Efficient Epistemic Uncertainty Estimation in Regression Ensemble Models Using Pairwise-Distance Estimatorscited by 1
  20. 2025Cooperative Variance Estimation and Bayesian Neural Networks for Disentangling Aleatoric and Epistemic Uncertaintiescited by 1
  21. 2025Epistemic Errors of Imperfect Multitask Learners When Distributions Shiftcited by 1
  22. 2025Representative, Informative, and De-Amplifying: Requirements for Robust Bayesian Active Learning under Model Misspecificationcited by 1
  23. 2026Set-based v.s. Distribution-based Representations of Epistemic Uncertainty: A Comparative Studycited by 1
  24. 2026A neurosymbolic Approach with Epistemic Deep Learning for Hierarchical Image Classificationcited by 1
  25. 2024On Uniform, Bayesian, and PAC-Bayesian Deep Ensemblescited by 0
  26. 2024Optimal Transport for ε-Contaminated Credal Sets: To the Memory of Sayan Mukherjeecited by 0
  27. 2025Empirical Decision Theorycited by 0
  28. 2026Robust Predictive Uncertainty and Double Descent in Contaminated Bayesian Random Featurescited by 0
  29. 2026Efficient Credal Prediction through Decalibrationcited by 0
  30. 2026Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantificationcited by 0
  31. 2026Decoupled Conformal Optimisation: Efficient Prediction Sets via Independent Tuning and Calibrationcited by 0
  32. 2026Conformalised imprecise inference for robust extrapolation under limited datacited by 0
  33. 2026Credal Machine Learning for Risk-Averse Decision Makingcited by 0