Subjective Risk Decomposition: A New View for Uncertainty Quantification

2026-07-16

AI Summary

This work addresses the lack of a unified theoretical foundation in traditional uncertainty quantification (UQ), which hinders systematic distinction between epistemic and aleatoric uncertainty. The authors propose a subjective risk decomposition framework that conceptualizes uncertainty as an emergent consequence of modeling choices. For the first time, this framework formally decomposes the two uncertainty types using strictly proper loss functions—such as reversed cross-entropy—grounded in rigorous statistical principles. By integrating information-theoretic analysis with excess risk decomposition from statistical learning theory, the approach not only recovers established uncertainty measures but also establishes novel theoretical connections between uncertainty quantification and the foundations of statistical learning.

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.

Problem

• uncertainty quantification
• epistemic uncertainty
• aleatoric uncertainty
• subjective risk
• proper loss

Innovation

• subjective risk decomposition
• uncertainty quantification
• strictly proper loss
• epistemic uncertainty
• aleatoric uncertainty