We present a novel viewpoint for uncertainty quantification. Uncertainty measures are not primitives but 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 classic information-theoretic uncertainty terms. This approach also recovers numerous measures previously proposed in the UQ literature, providing them a common theoretical foundation.
Practically, 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 extend our view to learning theory: we introduce and analyze subjective risk analogues of excess risk, approximation error, and estimation error, identifying connections to UQ.
We consider this a first step towards a full learning-theoretic framework for uncertainty quantification.
Blogger's Review: This paper redefines the foundations of uncertainty quantification through the decomposition of subjective risk, proposing a method that combines theoretical depth with practical applicability, especially in learning theory, where its potential applications are highly promising.