# Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?

arXiv: https://arxiv.org/abs/2402.09056 · HTML: https://mlsanity.com/paper/2402.09056/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 40 references that are in the map.
- First posted on arXiv 14 Feb 2024.

## Builds on (most cited first, 29 of 29)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods](https://mlsanity.com/paper/1910.09457/) (2019)
- [Evidential Deep Learning to Quantify Classification Uncertainty](https://mlsanity.com/paper/1806.01768/) (2018)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Your Classifier is Secretly an Energy Based Model and You Should Treat it Like One](https://mlsanity.com/paper/1912.03263/) (2019)
- [Deep Evidential Regression](https://mlsanity.com/paper/1910.02600/) (2019)
- [OpenOOD: Benchmarking Generalized Out-of-Distribution Detection](https://mlsanity.com/paper/2210.07242/) (2022)
- [A General Framework for Updating Belief Distributions](https://mlsanity.com/paper/1306.6430/) (2013)
- [Posterior Network: Uncertainty Estimation without OOD Samples via Density-Based Pseudo-Counts](https://mlsanity.com/paper/2006.09239/) (2020)
- [Quantifying Aleatoric and Epistemic Uncertainty in Machine Learning: Are Conditional Entropy and Mutual Information Appropriate Measures?](https://mlsanity.com/paper/2209.03302/) (2022)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [Evidential Deep Learning for Open Set Action Recognition](https://mlsanity.com/paper/2107.10161/) (2021)
- [Prior and Posterior Networks: A Survey on Evidential Deep Learning Methods For Uncertainty Estimation](https://mlsanity.com/paper/2110.03051/) (2021)
- [Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation](https://mlsanity.com/paper/2203.06102/) (2022)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable?](https://mlsanity.com/paper/2010.14986/) (2020)
- [Trustworthy Multimodal Regression with Mixture of Normal-inverse Gamma Distributions](https://mlsanity.com/paper/2111.08456/) (2021)
- [On Second-Order Scoring Rules for Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2301.12736/) (2023)
- [Second-Order Uncertainty Quantification: A Distance-Based Approach](https://mlsanity.com/paper/2312.00995/) (2023)
- [Regression Prior Networks](https://mlsanity.com/paper/2006.11590/) (2020)
- [Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty](https://mlsanity.com/paper/2311.08309/) (2023)
- [Multivariate Deep Evidential Regression](https://mlsanity.com/paper/2104.06135/) (2021)
- [Efficient and Robust LiDAR-Based End-to-End Navigation](https://mlsanity.com/paper/2105.09932/) (2021)
- [Second-Order Uncertainty Quantification: Variance-Based Measures](https://mlsanity.com/paper/2401.00276/) (2023)
- [Evidential Uncertainty Quantification: A Variance-Based Perspective](https://mlsanity.com/paper/2311.11367/) (2023)
- [Improving evidential deep learning via multi-task learning](https://mlsanity.com/paper/2112.09368/) (2021)
- [Evidential Conditional Neural Processes](https://mlsanity.com/paper/2212.00131/) (2022)
- [Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks](https://mlsanity.com/paper/2312.11230/) (2023)

## Built on by (most cited first, 30 of 35)

- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [Uncertainty Quantification for Machine Learning in Healthcare: A Survey](https://mlsanity.com/paper/2505.02874/) (2025)
- [Credal Wrapper of Model Averaging for Uncertainty Estimation in Classification](https://mlsanity.com/paper/2405.15047/) (2024)
- [Uncertainty Estimation by Flexible Evidential Deep Learning](https://mlsanity.com/paper/2510.18322/) (2025)
- [Provable Uncertainty Decomposition via Higher-Order Calibration](https://mlsanity.com/paper/2412.18808/) (2024)
- [Position: Epistemic uncertainty estimation methods are fundamentally incomplete](https://mlsanity.com/paper/2505.23506/) (2025)
- [Credal and Interval Deep Evidential Classifications](https://mlsanity.com/paper/2512.05526/) (2025)
- [A calibration test for evaluating set-based epistemic uncertainty representations](https://mlsanity.com/paper/2502.16299/) (2025)
- [Learning Credal Ensembles via Distributionally Robust Optimization](https://mlsanity.com/paper/2602.08470/) (2026)
- [Enhancing Uncertainty Quantification in Drug Discovery with Censored Regression Labels](https://mlsanity.com/paper/2409.04313/) (2024)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [Epistemic Wrapping for Uncertainty Quantification](https://mlsanity.com/paper/2505.02277/) (2025)
- [Uncertainty Quantification for Regression using Proper Scoring Rules](https://mlsanity.com/paper/2509.26610/) (2025)
- [Uncertainty in Physics and AI: Taxonomy, Quantification, and Validation](https://mlsanity.com/paper/2605.10378/) (2026)
- [Rethinking Approximate Gaussian Inference in Classification](https://mlsanity.com/paper/2502.03366/) (2025)
- [PRESCRIBE: Predicting Single-Cell Responses with Bayesian Estimation](https://mlsanity.com/paper/2510.07964/) (2025)
- [Deep Ensembles for Epistemic Uncertainty: A Frequentist Perspective](https://mlsanity.com/paper/2510.22063/) (2025)
- [Generalized Regularized Evidential Deep Learning Models: Theory and Comprehensive Evaluation](https://mlsanity.com/paper/2512.23753/) (2025)
- [Evidential Transformation Network: Turning Pretrained Models into Evidential Models for Post-hoc Uncertainty Estimation](https://mlsanity.com/paper/2604.08627/) (2026)
- [Uncertainties of Latent Representations in Computer Vision](https://mlsanity.com/paper/2408.14281/) (2024)
- [On Uncertainty Calibration for Equivariant Functions](https://mlsanity.com/paper/2510.21691/) (2025)
- [A formal definition and meta-model for a machine theory of mind](https://mlsanity.com/paper/2606.03471/) (2026)
- [A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Risk](https://mlsanity.com/paper/2608.05995/) (2026)
- [Principled Input-Output-Conditioned Post-Hoc Uncertainty Estimation for Regression Networks](https://mlsanity.com/paper/2506.00918/) (2025)
- [Foundations of Artificial Intelligence Frameworks: Notion and Limits of AGI](https://mlsanity.com/paper/2511.18517/) (2025)
- [Beyond a Single Signal: SPECTREG2, A Unified MultiExpert Anomaly Detector for Unknown Unknowns](https://mlsanity.com/paper/2603.21160/) (2026)
- [Do Not Imitate, Reinforce: Iterative Classification via Belief Refinement](https://mlsanity.com/paper/2604.22110/) (2026)
- [Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier](https://mlsanity.com/paper/2605.22746/) (2026)
- [Courtroom Analogy: New Perspective on Uncertainty-Aware Classification](https://mlsanity.com/paper/2605.25616/) (2026)
- [Can we trust our models? Epistemic calibration in second-order classification](https://mlsanity.com/paper/2606.10777/) (2026)

## Abstract (arXiv)

Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures.