Separating Prediction from Epistemic Uncertainty in Evidential Deep Learning

Evidential deep learning (EDL) predicts a Dirichlet distribution over class-probability vectors in a single forward pass, using its mean for prediction and its dispersion to represent epistemic uncertainty. However, class-label supervision directly informs the predictive mean but provides no direct target for the dispersion. Standard EDL nevertheless uses the same labels to learn both, creating a *supervision–estimand mismatch*: the objective intended to shape dispersion lacks a direct dispersion supervision and can also alter the predictive mean. We address this mismatch with *Bayesian Evidential Dispersion Inference* (BEDI), a probabilistic framework that separates predictive-mean estimation from dispersion inference. BEDI fixes the Dirichlet mean at the calibrated predictive mean of a trained classifier, preserving its class probabilities and predictions by construction. It then infers dispersion using two complementary signals: effective sample size, which quantifies the training information relevant to an input, and Bayesian predictive disagreement, which reflects variation in class probabilities under model uncertainty. Through hierarchical dispersion inference, BEDI uses effective sample size to define a prior over input-specific dispersion and predictive disagreement to update this prior, while learning a shared relationship between effective sample size and dispersion across inputs. This shared relationship enables dispersion inference at new inputs with a single neural-network forward pass. Our theoretical analysis formalizes the supervision–estimand mismatch and establishes contraction of epistemic uncertainty as effective sample size increases. Across standard and long-tailed classification benchmarks and pretrained-model settings, BEDI achieves strong performance on a range of downstream tasks requiring reliable uncertainty quantification.