Subjective Risk Decomposition: A New View for Uncertainty Quantification
Artificial IntelligenceMachine Learning
Summary
The authors propose a new way to think about measuring uncertainty that doesn't start with predefined rules but instead derives uncertainty from modeling choices. They show how two types of uncertainty—epistemic (due to lack of knowledge) and aleatoric (due to randomness)—can be broken down from a subjective risk related to a special type of loss function. Their approach connects many previous uncertainty measures into one common theory. They also explore how this idea relates to learning theory by introducing risk-based concepts that link to uncertainty. This work aims to build a more complete framework for understanding uncertainty in models.
Authors
Raghad Alamri, Michele Caprio, Gavin Brown
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.