mlsanityData to 14 Oct 2026

From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation

arXiv 2402.10727 ↗First posted 16 Feb 2024stat.ML cs.LGcited by 28

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Abstract (arXiv)

There are various measures of predictive uncertainty in the literature, but their relationships to each other remain unclear. This paper uses a decomposition of statistical pointwise risk into components, associated with different sources of predictive uncertainty, namely aleatoric uncertainty (inherent data variability) and epistemic uncertainty (model-related uncertainty). Together with Bayesian methods, applied as an approximation, we build a framework that allows one to generate different predictive uncertainty measures. We validate our method on image datasets by evaluating its performance in detecting out-of-distribution and misclassified instances using the AUROC metric. The experimental results confirm that the measures derived from our framework are useful for the considered downstream tasks.

Key facts. Cited by 28 papers in the map (data through 14 Oct 2026). Builds on 38 of its 55 references that are in the map. First posted on arXiv 16 Feb 2024.

Builds on

38 of 55 references.

References · 38

  1. 2015Deep Residual Learning for Image Recognitioncited by 52,096
  2. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
  3. 2016Simple and Scalable Predictive Uncertainty Estimation using Deep Ensemblescited by 3,926
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,352
  5. 2020The Many Faces of Robustness: A Critical Analysis of Out-of-Distribution Generalizationcited by 1,850
  6. 2016Variational Inference: A Review for Statisticianscited by 1,472
  7. 2019Natural Adversarial Examplescited by 1,408
  8. 2020Energy-based Out-of-distribution Detectioncited by 1,299
  9. 2017A Survey on Deep Learning in Medical Image Analysiscited by 1,186
  10. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 913
  11. 2017Selective Classification for Deep Neural Networkscited by 852
  12. 2017Deep Bayesian Active Learning with Image Datacited by 819
26 more
  1. 2018Predictive Uncertainty Estimation via Prior Networkscited by 557
  2. 2019Your Classifier is Secretly an Energy Based Model and You Should Treat it Like Onecited by 405
  3. 2019A Survey of Deep Learning Techniques for Autonomous Drivingcited by 403
  4. 2017Deep Learning for Medical Image Analysiscited by 401
  5. 2020Simple and Principled Uncertainty Estimation with Deterministic Deep Learning via Distance Awarenesscited by 389
  6. 2021What Are Bayesian Neural Network Posteriors Really Like?cited by 308
  7. 2021Deep Deterministic Uncertainty: A Simple Baselinecited by 200
  8. 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 125
  9. 2021DEUP: Direct Epistemic Uncertainty Predictioncited by 104
  10. 2020Deep Learning for Financial Applications : A Surveycited by 91
  11. 2024Estimating Epistemic and Aleatoric Uncertainty with a Single Modelcited by 54
  12. 2022On Uncertainty, Tempering, and Data Augmentation in Bayesian Classificationcited by 46
  13. 2019Accurate Uncertainty Estimation and Decomposition in Ensemble Learningcited by 42
  14. 2023On Second-Order Scoring Rules for Epistemic Uncertainty Quantificationcited by 38
  15. 2021Monte Carlo Variational Auto-Encoderscited by 36
  16. 2022Nonparametric Uncertainty Quantification for Single Deterministic Neural Networkcited by 36
  17. 2022FedPop: A Bayesian Approach for Personalised Federated Learningcited by 35
  18. 2023Quantification of Uncertainty with Adversarial Modelscited by 28
  19. 2023Introducing an Improved Information-Theoretic Measure of Predictive Uncertaintycited by 28
  20. 2018Dropout-based Active Learning for Regressioncited by 24
  21. 2022Uncertainty Estimates of Predictions via a General Bias-Variance Decompositioncited by 20
  22. 2023A Novel Bayes' Theorem for Upper Probabilitiescited by 13
  23. 2022Understanding the bias-variance tradeoff of Bregman divergencescited by 11
  24. 2023Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networkscited by 8
  25. 2020MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inferencecited by 7
  26. 2020Dropout Strikes Back: Improved Uncertainty Estimation via Diversity Samplingcited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 5; 2025: 13; 2026: 10.

28 papers.

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  1. 2024Rethinking Aleatoric and Epistemic Uncertaintycited by 42
  2. 2025Uncertainty Quantification for LLMs through Minimum Bayes Risk: Bridging Confidence and Consistencycited by 30
  3. 2024Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rulescited by 21
  4. 2024Rethinking Uncertainty Estimation in LLMs: A Principled Single-Sequence Measurecited by 18
  5. 2025The Illusion of Certainty: Uncertainty Quantification for LLMs Fails under Ambiguitycited by 17
  6. 2024On Information-Theoretic Measures of Predictive Uncertaintycited by 16
  7. 2025Uncertainty Quantification for Hallucination Detection in Large Language Models: Foundations, Methodology, and Future Directionscited by 11
  8. 2024Provable Uncertainty Decomposition via Higher-Order Calibrationcited by 9
  9. 2025An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regressioncited by 9
  10. 2025Addressing Pitfalls in the Evaluation of Uncertainty Estimation Methods for Natural Language Generationcited by 7
  11. 2025Uncertainty as Feature Gaps: Epistemic Uncertainty Quantification of LLMs in Contextual Question-Answeringcited by 7
  12. 2026ReDAct: Uncertainty-Aware Deferral for LLM Agentscited by 7
16 more
  1. 2025UNCERTAINTY-LINE: Length-Invariant Estimation of Uncertainty for Large Language Modelscited by 5
  2. 2025Uncertainty Quantification for Regression using Proper Scoring Rulescited by 5
  3. 2026Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilitiescited by 5
  4. 2025Uncertainty Quantification for Machine Learning: One Size Does Not Fit Allcited by 4
  5. 2025Deep Ensembles for Epistemic Uncertainty: A Frequentist Perspectivecited by 2
  6. 2025Uncertainty Quantification for Regression: A Unified Framework based on kernel scorescited by 2
  7. 2026Evaluating Epistemic Uncertainty: Beyond OOD Detection and Active Learningcited by 2
  8. 2025Uncertainty Quantification with Proper Scoring Rules: Adjusting Measures to Prediction Taskscited by 1
  9. 2025Multidimensional Uncertainty Quantification via Optimal Transportcited by 1
  10. 2026Subjective Risk Decomposition: A New View for Uncertainty Quantificationcited by 1
  11. 2026A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Riskcited by 1
  12. 2026On the QUEST for Uncertainty Quantification via Highest Density Regionscited by 0
  13. 2026Code-MUE: Measuring Code LLMs' Uncertainty through Execution-based Semantic Interaction Graphscited by 0
  14. 2026Decomposing LLM-Judge Uncertainty to Target Expert Labelscited by 0
  15. 2026Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Studycited by 0
  16. 2026Uncertainty Evaluation: Bridging Machine Learning and Measurement Sciencecited by 0