Subjective Risk Decomposition: A New View for Uncertainty Quantification

A Unified View of Uncertainty

Uncertainty quantification (UQ) in machine learning has historically been fragmented, with researchers proposing various, often competing, definitions for aleatoric and epistemic uncertainty. This paper argues that these measures should not be treated as fundamental primitives requiring separate axiomatic justifications. Instead, the authors propose that they are natural consequences of higher-level modeling decisions—specifically, the choice of a strictly proper loss function used to evaluate a model.

The Subjective Risk Framework

The authors introduce a methodology based on the decision-theoretic concept of subjective risk. By decomposing the expected subjective risk—the loss evaluated under the agent's own beliefs rather than the true data-generating distribution—the authors derive a reverse bias–variance decomposition. This decomposition naturally yields terms that correspond to epistemic and aleatoric uncertainty.

Crucially, this approach demonstrates that the classic information-theoretic framework (e.g., mutual information for epistemic uncertainty and entropy for aleatoric uncertainty) is simply the result of applying this decomposition to the reverse cross-entropy. By varying the loss function, the authors show that many other previously proposed UQ measures emerge as special cases of this same underlying principle.

Bridging UQ and Learning Theory

The paper extends this viewpoint into statistical learning theory by defining subjective risk analogues for standard concepts such as excess risk, approximation error, and estimation error. This connection highlights how epistemic uncertainty is fundamentally intertwined with the model's estimation error. By framing UQ within this broader statistical context, the authors provide a foundation for future research that treats uncertainty not as an isolated metric, but as a core component of the learning process itself.