mlsanityData to 7 Oct 2026

Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?

arXiv 2209.03302 ↗First posted 7 Sep 2022cs.LGcited by 124

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Abstract (arXiv)

The quantification of aleatoric and epistemic uncertainty in terms of conditional entropy and mutual information, respectively, has recently become quite common in machine learning. While the properties of these measures, which are rooted in information theory, seem appealing at first glance, we identify various incoherencies that call their appropriateness into question. In addition to the measures themselves, we critically discuss the idea of an additive decomposition of total uncertainty into its aleatoric and epistemic constituents. Experiments across different computer vision tasks support our theoretical findings and raise concerns about current practice in uncertainty quantification.

Key facts. Cited by 124 papers in the map (data through 7 Oct 2026). Builds on 29 of its 59 references that are in the map. First posted on arXiv 7 Sep 2022.

Builds on

29 of 59 references.

References · 29

  1. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  2. 2019EfficientNet: Rethinking Model Scaling for Convolutional Neural Networkscited by 6,415
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,888
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  5. 2019Can You Trust Your Model's Uncertainty? Evaluating Predictive Uncertainty Under Dataset Shiftcited by 1,274
  6. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  7. 2017Deep Bayesian Active Learning with Image Datacited by 812
  8. 2018Predictive Uncertainty Estimation via Prior Networkscited by 555
  9. 2021Laplace Redux -- Effortless Bayesian Deep Learningcited by 359
  10. 2020Pitfalls of In-Domain Uncertainty Estimation and Ensembling in Deep Learningcited by 208
  11. 2018Understanding Measures of Uncertainty for Adversarial Example Detectioncited by 177
  12. 2022Uncertainty Quantification in Scientific Machine Learning: Methods, Metrics, and Comparisonscited by 169
17 more
  1. 2020Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Countscited by 163
  2. 2019Ensemble Distribution Distillationcited by 158
  3. 2019A Survey on Active Learning and Human-in-the-Loop Deep Learning for Medical Image Analysiscited by 150
  4. 2020SUNRISE: A Simple Unified Framework for Ensemble Learning in Deep Reinforcement Learningcited by 150
  5. 2019Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustnesscited by 104
  6. 2019DropConnect Is Effective in Modeling Uncertainty of Bayesian Deep Networkscited by 92
  7. 2020The Case for Bayesian Deep Learningcited by 68
  8. 2022Deep Ensembles Work, But Are They Necessary?cited by 63
  9. 2018Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Controlcited by 54
  10. 2020Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable?cited by 39
  11. 2021Active Learning for Sequence Tagging with Deep Pre-trained Models and Bayesian Uncertainty Estimatescited by 39
  12. 2022Disentangling Epistemic and Aleatoric Uncertainty in Reinforcement Learningcited by 27
  13. 2022FiLM-Ensemble: Probabilistic Deep Learning via Feature-wise Linear Modulationcited by 24
  14. 2021Being a Bit Frequentist Improves Bayesian Neural Networkscited by 15
  15. 2017Decomposition of Uncertainty in Bayesian Deep Learning for Efficient and Risk-sensitive Learningcited by 5
  16. 2022Analytic Mutual Information in Bayesian Neural Networkscited by 5
  17. 2022Marginal and Joint Cross-Entropies & Predictives for Online Bayesian Inference, Active Learning, and Active Samplingcited by 3

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 1; 2023: 12; 2024: 41; 2025: 35; 2026: 35.

124 papers.

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  1. 2024Benchmarking Uncertainty Disentanglement: Specialized Uncertainties for Specialized Taskscited by 78
  2. 2024Do LLMs Know When to NOT Answer? Investigating Abstention Abilities of Large Language Modelscited by 55
  3. 2024A Survey of Uncertainty Estimation in LLMs: Theory Meets Practicecited by 54
  4. 2024Uncertainty Quantification for In-Context Learning of Large Language Modelscited by 45
  5. 2023Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?cited by 40
  6. 2024Rethinking Aleatoric and Epistemic Uncertaintycited by 40
  7. 2023Explaining Predictive Uncertainty with Information Theoretic Shapley Valuescited by 36
  8. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  9. 2024Uncertainty quantification in fine-tuned LLMs using LoRA ensemblescited by 35
  10. 2024Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?cited by 34
  11. 2024Active Evaluation Acquisition for Efficient LLM Benchmarkingcited by 33
  12. 2024On the Challenges and Opportunities in Generative AIcited by 31
38 more
  1. 2023Introducing an Improved Information-Theoretic Measure of Predictive Uncertaintycited by 28
  2. 2024From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimationcited by 27
  3. 2025Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agentscited by 27
  4. 2024A Comprehensive Survey on Evidential Deep Learning and Its Applicationscited by 25
  5. 2024Label-wise Aleatoric and Epistemic Uncertainty Quantificationcited by 22
  6. 2024Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rulescited by 21
  7. 2023Second-Order Uncertainty Quantification: Variance-Based Measurescited by 19
  8. 2024Conformalized Credal Regions for Classification with Ambiguous Ground Truthcited by 19
  9. 2024On Information-Theoretic Measures of Predictive Uncertaintycited by 16
  10. 2024(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Modelscited by 15
  11. 2025The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguitycited by 15
  12. 2023A Novel Bayes' Theorem for Upper Probabilitiescited by 13
  13. 2024Scalable Bayesian Learning with posteriorscited by 13
  14. 2026Knowing When to Abstain: Medical LLMs Under Clinical Uncertaintycited by 13
  15. 2025Integral Imprecise Probability Metricscited by 11
  16. 2024Pretrained Visual Uncertaintiescited by 10
  17. 2023Laplacian Segmentation Networks Improve Epistemic Uncertainty Quantificationcited by 9
  18. 2024A Structured Review of Literature on Uncertainty in Machine Learning & Deep Learningcited by 9
  19. 2025An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regressioncited by 9
  20. 2025Grammars of Formal Uncertainty: When to Trust LLMs in Automated Reasoning Taskscited by 9
  21. 2023Multi-Head Multi-Loss Model Calibrationcited by 8
  22. 2024Are We Ready for Out-of-Distribution Detection in Digital Pathology?cited by 8
  23. 2024Function Space Diversity for Uncertainty Prediction via Repulsive Last-Layer Ensemblescited by 8
  24. 2024Provable Uncertainty Decomposition via Higher-Order Calibrationcited by 8
  25. 2025Position: Epistemic uncertainty estimation methods are fundamentally incompletecited by 8
  26. 2023Ensembled Prediction Intervals for Causal Outcomes Under Hidden Confoundingcited by 7
  27. 2023Uncertainty Quantification in Machine Learning for Biosignal Applications -- A Reviewcited by 7
  28. 2025Conformal Prediction Regions are Imprecise Highest Density Regionscited by 7
  29. 2023Model-agnostic variable importance for predictive uncertainty: an entropy-based approachcited by 6
  30. 2024A Review of Bayesian Uncertainty Quantification in Deep Probabilistic Image Segmentationcited by 6
  31. 2024Federated Continual Learning Goes Online: Uncertainty-Aware Memory Management for Vision Tasks and Beyondcited by 5
  32. 2025Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisitioncited by 5
  33. 2025Uncertainty Quantification for Regression using Proper Scoring Rulescited by 5
  34. 2024Measuring Orthogonality as the Blind-Spot of Uncertainty Disentanglementcited by 4
  35. 2024Stochasticity in Motion: An Information-Theoretic Approach to Trajectory Predictioncited by 4
  36. 2024Improving Active Learning with a Bayesian Representation of Epistemic Uncertaintycited by 4
  37. 2025Delusions of Large Language Modelscited by 4
  38. 2025Revisiting Active Learning under (Human) Label Variationcited by 4

50 most cited of 124 All 124 (JSON)