Subjective Risk Decomposition: A New View for Uncertainty Quantification

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.

Machine Learning (stat.ML); Artificial Intelligence (cs.AI); Machine Learning (cs.LG)

arXiv:2607.15196 [stat.ML]

(or arXiv:2607.15196v2 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2607.15196 Focus to learn more arXiv-issued DOI via DataCite

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