Subjective Risk Decomposition: A New View for Uncertainty Quantification
stat.ML, cs.AI, cs.LG
Submitted: 2026-07-16
Updated: 2026-09-16
Comments: 36 pages (including bibliography/appendix)
License: http://creativecommons.org/licenses/by/4.0/
The gist: We present a novel viewpoint for uncertainty quantification.
Terminology
Abstract
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.
Sources
- An Axiomatic Assessment of Entropy- and Variance-based Uncertainty Quantification in Regression
- Uncertainty Quantification for Regression using Proper Scoring Rules
- Uncertainty Estimates of Predictions via a General Bias-Variance Decomposition
- Bias-variance decompositions: the exclusive privilege of Bregman divergences
- Quantifying Aleatoric and Epistemic Uncertainty with Proper Scoring Rules
- Quantifying Epistemic Uncertainty in Deep Learning
- Efficient Uncertainty Quantification and Reduction for Over-Parameterized Neural Networks
- A Generalized Bias-Variance Decomposition for Bregman Divergences
- Introducing an Improved Information-Theoretic Measure of Predictive Uncertainty
- Iterative Preference Learning from Human Feedback: Bridging Theory and Practice for RLHF under KL-Constraint
- Fine-Tuning Language Models from Human Preferences
Related papers
- Behavior of prediction performance metrics with rare events
- Optimal Estimation of Generic Dynamics by Path-Dependent Neural Jump ODEs
- A Posterior-Dynamics Framework for Imaging Inverse Problems with Pretrained Diffusion Priors
- Scalable Posterior Uncertainty for Flexible Density-Based Clustering
- A Transport Geometry of Benign Overfitting
- Efficient quadratic entropy with distance sketches