mlsanityData to 7 Oct 2026

Second-Order Uncertainty Quantification: Variance-Based Measures

arXiv 2401.00276 ↗First posted 30 Dec 2023cs.LG stat.MLcited by 19

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Abstract (arXiv)

Uncertainty quantification is a critical aspect of machine learning models, providing important insights into the reliability of predictions and aiding the decision-making process in real-world applications. This paper proposes a novel way to use variance-based measures to quantify uncertainty on the basis of second-order distributions in classification problems. A distinctive feature of the measures is the ability to reason about uncertainties on a class-based level, which is useful in situations where nuanced decision-making is required. Recalling some properties from the literature, we highlight that the variance-based measures satisfy important (axiomatic) properties. In addition to this axiomatic approach, we present empirical results showing the measures to be effective and competitive to commonly used entropy-based measures.

Key facts. Cited by 19 papers in the map (data through 7 Oct 2026). Builds on 19 of its 43 references that are in the map. First posted on arXiv 30 Dec 2023.

Builds on

19 of 43 references.

References · 19

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
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  3. 2019PyTorch: An Imperative Style, High-Performance Deep Learning Librarycited by 20,160
  4. 2017What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?cited by 2,335
  5. 2019Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methodscited by 903
  6. 2018Deep Learning for Classical Japanese Literaturecited by 415
  7. 2018Understanding Measures of Uncertainty for Adversarial Example Detectioncited by 177
  8. 2022Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?cited by 124
  9. 2019DropConnect Is Effective in Modeling Uncertainty of Bayesian Deep Networkscited by 92
  10. 2021Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimationcited by 71
  11. 2018Evaluating Uncertainty Quantification in End-to-End Autonomous Driving Controlcited by 54
  12. 2016On the Safety of Machine Learning: Cyber-Physical Systems, Decision Sciences, and Data Productscited by 52
7 more
  1. 2021Active Learning for Sequence Tagging with Deep Pre-trained Models and Bayesian Uncertainty Estimatescited by 39
  2. 2023Second-Order Uncertainty Quantification: A Distance-Based Approachcited by 35
  3. 2022Bayesian Optimization with Conformal Prediction Setscited by 27
  4. 2023Sources of Uncertainty in Supervised Machine Learning -- A Statisticians' Viewcited by 27
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  6. 2023Evidential Uncertainty Quantification: A Variance-Based Perspectivecited by 14
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 9; 2025: 6; 2026: 4.

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  1. 2024Rethinking Aleatoric and Epistemic Uncertaintycited by 40
  2. 2024Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?cited by 34
  3. 2024A Comprehensive Survey on Evidential Deep Learning and Its Applicationscited by 25
  4. 2024Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rulescited by 21
  5. 2024On Information-Theoretic Measures of Predictive Uncertaintycited by 16
  6. 2024Revisiting Essential and Nonessential Settings of Evidential Deep Learningcited by 15
  7. 2025Integral Imprecise Probability Metricscited by 11
  8. 2024Provable Uncertainty Decomposition via Higher-Order Calibrationcited by 8
  9. 2025Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisitioncited by 5
  10. 2024Linear Opinion Pooling for Uncertainty Quantification on Graphscited by 2
  11. 2025Uncertainty Quantification for Regression: A Unified Framework based on kernel scorescited by 2
  12. 2025Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluationcited by 2
7 more
  1. 2026An Isotropic Approach to Efficient Uncertainty Quantification with Gradient Normscited by 1
  2. 2026Tracing Uncertainty in Language Model "Reasoning"cited by 1
  3. 2026Subjective Risk Decomposition: A New View for Uncertainty Quantificationcited by 1
  4. 2024CUQ-GNN: Committee-based Graph Uncertainty Quantification using Posterior Networkscited by 0
  5. 2025On Measuring Intrinsic Causal Attributions in Deep Neural Networkscited by 0
  6. 2025Principled Input-Output-Conditioned Post-Hoc Uncertainty Estimation for Regression Networkscited by 0
  7. 2026A Risk-Sensitive and Uncertainty-Aware Decision-Making and Control Framework for Safe and Robust Autonomous Drivingcited by 0