# Subjective Risk Decomposition: A New View for Uncertainty Quantification

arXiv: https://arxiv.org/abs/2607.15196 · HTML: https://mlsanity.com/paper/2607.15196/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 51 references that are in the map.
- First posted on arXiv 16 Jul 2026.

## Builds on (most cited first, 26 of 26)

- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint](https://mlsanity.com/paper/2312.11456/) (2023)
- [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)
- [DEUP: Direct Epistemic Uncertainty Prediction](https://mlsanity.com/paper/2102.08501/) (2021)
- [A Deeper Look into Aleatoric and Epistemic Uncertainty Disentanglement](https://mlsanity.com/paper/2204.09308/) (2022)
- [A Unified Theory of Diversity in Ensemble Learning](https://mlsanity.com/paper/2301.03962/) (2023)
- [Aleatoric and Epistemic Uncertainty with Random Forests](https://mlsanity.com/paper/2001.00893/) (2020)
- [Rethinking Aleatoric and Epistemic Uncertainty](https://mlsanity.com/paper/2412.20892/) (2024)
- [Nonparametric Uncertainty Quantification for Single Deterministic Neural Network](https://mlsanity.com/paper/2202.03101/) (2022)
- [Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty](https://mlsanity.com/paper/2311.08309/) (2023)
- [From Risk to Uncertainty: Generating Predictive Uncertainty Measures via Bayesian Estimation](https://mlsanity.com/paper/2402.10727/) (2024)
- [Label-wise Aleatoric and Epistemic Uncertainty Quantification](https://mlsanity.com/paper/2406.02354/) (2024)
- [Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules](https://mlsanity.com/paper/2404.12215/) (2024)
- [Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition](https://mlsanity.com/paper/2210.12256/) (2022)
- [Second-Order Uncertainty Quantification: Variance-Based Measures](https://mlsanity.com/paper/2401.00276/) (2023)
- [Quantifying Epistemic Uncertainty in Deep Learning](https://mlsanity.com/paper/2110.12122/) (2021)
- [Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks](https://mlsanity.com/paper/2306.05674/) (2023)
- [An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression](https://mlsanity.com/paper/2504.18433/) (2025)
- [Position: Epistemic uncertainty estimation methods are fundamentally incomplete](https://mlsanity.com/paper/2505.23506/) (2025)
- [A Generalized Bias-Variance Decomposition for Bregman Divergences](https://mlsanity.com/paper/2511.08789/) (2025)
- [Bias-variance decompositions: the exclusive privilege of Bregman divergences](https://mlsanity.com/paper/2501.18581/) (2025)
- [Uncertainty Quantification for Regression using Proper Scoring Rules](https://mlsanity.com/paper/2509.26610/) (2025)

## Built on by (most cited first, 1 of 1)

- [A Ground-Truth Framework for Uncertainty Disentanglement with Posterior Risk](https://mlsanity.com/paper/2608.05995/) (2026)

## Abstract (arXiv)

We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives, in need of axioms and argumentation, but instead consequences, of higher-level modelling decisions. We show how epistemic and aleatoric uncertainty measures can be derived via decomposition of a subjective risk, based on a strictly proper loss. Reverse cross entropy provides a prominent example, where decomposition recovers the classic information-theoretic uncertainty terms. The same approach recovers numerous measures previously proposed across the UQ literature, providing them a common theoretical foundation. This suggests a new approach to UQ: given a modelling scenario and strictly proper loss, the corresponding epistemic and aleatoric terms are induced by the subjective-risk decomposition. We then extend our view to learning theory: we introduce and analyse subjective risk analogues of excess risk, approximation error and estimation error, and identify the connections to UQ. We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.