Subjective Risk Decomposition: A New View for Uncertainty Quantification

arXiv paper (cs.AI) · Raghad Alamri, Michele Caprio, Gavin Brown

This paper provides a unifying mathematical framework that derives uncertainty quantification measures from first principles (proper losses) rather than treating them as ad-hoc definitions, which means you can now choose your uncertainty decomposition systematically based on your actual modeling objective instead of picking among disconnected existing methods. It directly connects loss functions to epistemic/aleatoric uncertainty, giving you a principled way to design UQ approaches for your specific application rather than applying generic formulas.

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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