Subjective Risk Decomposition: A New View for Uncertainty Quantification

• URL: http://arxiv.org/abs/2607.15196v1
• Date: Thu, 16 Jul 2026 16:52:54 GMT
• Title: Subjective Risk Decomposition: A New View for Uncertainty Quantification
• Abstract summary: We show how uncertainty measures can be derived via decomposition of a subjective risk.<n>Reverse cross-entropy provides a prominent example.<n>We then extend our view to learning theory.
• Score: 3.3198034832456345
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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