ArXiv

Subjective Risk Decomposition: A New View for Uncertainty Quantification

2026-07-16 · 16:52 UTC ·Raghad Alamri, Michele Caprio, Gavin Brown ·1 min read
Authors
Raghad Alamri, Michele Caprio, Gavin Brown
Categories
stat.ML, cs.AI, cs.LG
arXiv
https://arxiv.org/abs/2607.15196v1
PDF
https://arxiv.org/pdf/2607.15196v1

Brief

Subjective Risk Decomposition presents a framework that derives epistemic and aleatoric uncertainty as consequences of modelling choices by decomposing a subjective risk defined via a strictly proper loss. Using reverse cross-entropy it recovers classic information-theoretic uncertainty terms and subsumes many prior UQ measures; it also proposes learning-theoretic analogues (excess, approximation, estimation error).

Why it matters

Subjective-risk decomposition: Alamri, Caprio, and Brown (arXiv:2607.15196v1, published 2026-07-16) show epistemic and aleatoric uncertainty can be derived as consequences of modelling choices by decomposing a subjective risk specified by a strictly proper loss; reverse cross-entropy recovers classic information-theoretic uncertainty terms.

Key details

  • Practical and theoretical impact: the framework subsumes numerous existing UQ measures, prescribes that given a modelling scenario + strictly proper loss the epistemic/aleatoric terms are induced, and introduces subjective-risk analogues of excess risk, approximation error, and estimation error (27-page paper).
Source evidence

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. From a practical point of view, 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.

Comment: 27 pages (including bibliography/appendix)