# Pitfalls of Epistemic Uncertainty Quantification through Loss Minimisation

arXiv: https://arxiv.org/abs/2203.06102 · HTML: https://mlsanity.com/paper/2203.06102/

## Key facts

- Cited by 66 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 11 Mar 2022.

## Builds on (most cited first, 14 of 14)

- [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)
- [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)
- [Ensemble Distribution Distillation](https://mlsanity.com/paper/1905.00076/) (2019)
- [Reverse KL-Divergence Training of Prior Networks: Improved Uncertainty and Adversarial Robustness](https://mlsanity.com/paper/1905.13472/) (2019)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [On the Safety of Machine Learning: Cyber-Physical Systems, Decision Sciences, and Data Products](https://mlsanity.com/paper/1610.01256/) (2016)
- [Aleatoric and Epistemic Uncertainty with Random Forests](https://mlsanity.com/paper/2001.00893/) (2020)
- [Evaluating Robustness of Predictive Uncertainty Estimation: Are Dirichlet-based Models Reliable?](https://mlsanity.com/paper/2010.14986/) (2020)
- [Engineering Safety in Machine Learning](https://mlsanity.com/paper/1601.04126/) (2016)
- [Concave losses for robust dictionary learning](https://mlsanity.com/paper/1711.00659/) (2017)

## Built on by (most cited first, 30 of 66)

- [Uncertainty Estimation by Fisher Information-based Evidential Deep Learning](https://mlsanity.com/paper/2303.02045/) (2023)
- [Estimating Epistemic and Aleatoric Uncertainty with a Single Model](https://mlsanity.com/paper/2402.03478/) (2024)
- [The Unreasonable Effectiveness of Deep Evidential Regression](https://mlsanity.com/paper/2205.10060/) (2022)
- [Is the Volume of a Credal Set a Good Measure for Epistemic Uncertainty?](https://mlsanity.com/paper/2306.09586/) (2023)
- [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)
- [Is Epistemic Uncertainty Faithfully Represented by Evidential Deep Learning Methods?](https://mlsanity.com/paper/2402.09056/) (2024)
- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [A Comprehensive Survey on Evidential Deep Learning and Its Applications](https://mlsanity.com/paper/2409.04720/) (2024)
- [Conformalized Credal Set Predictors](https://mlsanity.com/paper/2402.10723/) (2024)
- [Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules](https://mlsanity.com/paper/2404.12215/) (2024)
- [Random-Set Neural Networks (RS-NN)](https://mlsanity.com/paper/2307.05772/) (2023)
- [Experts Don't Cheat: Learning What You Don't Know By Predicting Pairs](https://mlsanity.com/paper/2402.08733/) (2024)
- [Conformalized Credal Regions for Classification with Ambiguous Ground Truth](https://mlsanity.com/paper/2411.04852/) (2024)
- [Are Uncertainty Quantification Capabilities of Evidential Deep Learning a Mirage?](https://mlsanity.com/paper/2402.06160/) (2024)
- [(Implicit) Ensembles of Ensembles: Epistemic Uncertainty Collapse in Large Models](https://mlsanity.com/paper/2409.02628/) (2024)
- [Revisiting Essential and Nonessential Settings of Evidential Deep Learning](https://mlsanity.com/paper/2410.00393/) (2024)
- [Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement](https://mlsanity.com/paper/2306.12803/) (2023)
- [Hyper Evidential Deep Learning to Quantify Composite Classification Uncertainty](https://mlsanity.com/paper/2404.10980/) (2024)
- [Uncertainty Estimation by Flexible Evidential Deep Learning](https://mlsanity.com/paper/2510.18322/) (2025)
- [Proper Scoring Rules for Survival Analysis](https://mlsanity.com/paper/2305.00621/) (2023)
- [Provable Uncertainty Decomposition via Higher-Order Calibration](https://mlsanity.com/paper/2412.18808/) (2024)
- [Conformal Prediction and Human Decision Making](https://mlsanity.com/paper/2503.11709/) (2025)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [Dirichlet-based Uncertainty Quantification for Personalized Federated Learning with Improved Posterior Networks](https://mlsanity.com/paper/2312.11230/) (2023)
- [Epistemic Artificial Intelligence is Essential for Machine Learning Models to Truly 'Know When They Do Not Know'](https://mlsanity.com/paper/2505.04950/) (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)
- [Reducing Aleatoric and Epistemic Uncertainty through Multi-modal Data Acquisition](https://mlsanity.com/paper/2501.18268/) (2025)
- [Revisiting Active Learning under (Human) Label Variation](https://mlsanity.com/paper/2507.02593/) (2025)

## Abstract (arXiv)

Uncertainty quantification has received increasing attention in machine learning in the recent past. In particular, a distinction between aleatoric and epistemic uncertainty has been found useful in this regard. The latter refers to the learner's (lack of) knowledge and appears to be especially difficult to measure and quantify. In this paper, we analyse a recent proposal based on the idea of a second-order learner, which yields predictions in the form of distributions over probability distributions. While standard (first-order) learners can be trained to predict accurate probabilities, namely by minimising suitable loss functions on sample data, we show that loss minimisation does not work for second-order predictors: The loss functions proposed for inducing such predictors do not incentivise the learner to represent its epistemic uncertainty in a faithful way.