Not Just How Much, But Where: Decomposing Epistemic Uncertainty into Per-Class Contributions

Abstract

In safety-critical classification, the cost of failure is often asymmetric. Yet Bayesian deep learning summarises epistemic uncertainty with a single scalar, mutual information (MI), which cannot distinguish whether a model’s ignorance involves a benign or safety-critical class. We decompose MI into a per-class vector 𝒞_k(x)=σ_k^2/(2μ_k), with μ_k = 𝔼[p_k] and σ_k^2 = Var[p_k] across posterior samples. The decomposition follows from a second-order Taylor expansion of the entropy; the 1/μ_k weighting corrects boundary suppression and makes 𝒞_k comparable across rare and common classes. By construction ∑_k 𝒞_k ≈MI, and a companion skewness diagnostic flags inputs where the approximation degrades. After characterising the axiomatic properties of 𝒞_k, we validate it on three tasks: (i) selective prediction for diabetic retinopathy, where critical-class 𝒞_k reduces selective risk by 34.7