Subjective Risk Decomposition: A New View for Uncertainty Quantification
The paper provides a unifying theoretical framework for uncertainty quantification, which is relevant for researchers and practitioners in machine learning and statistics seeking a principled foundation for UQ methods.
The paper proposes a new viewpoint for uncertainty quantification (UQ) where epistemic and aleatoric uncertainty measures are derived from decomposing a subjective risk based on a strictly proper loss. This approach unifies numerous existing UQ measures under a common theoretical foundation and extends to learning theory by introducing subjective risk analogues of excess risk, approximation error, and estimation error.
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.