Evidential Uncertainty in Deep Learning

• Evidential uncertainty quantification is a method that models a meta-distribution over predictions, capturing both aleatoric and epistemic uncertainty.
• It employs neural networks to output parameters for conjugate priors, such as Dirichlet for classification, ensuring computational efficiency.
• This technique is vital for tasks like out-of-distribution detection and selective classification, though limitations in epistemic quantification are under active study.

Evidential uncertainty quantification refers to a family of techniques, principally typified by the Evidential Deep Learning (EDL) framework, in which a neural network is trained to predict not just pointwise predictive probabilities or regression outputs, but a higher-order distribution over such predictions—termed a “meta-distribution” or “evidential distribution.” This permits the estimation of both aleatoric (data) and epistemic (model) uncertainty from a single deterministic forward pass, via outputting parameters of a conjugate prior (Dirichlet for classification, Normal–Inverse-Gamma for regression) instead of direct target estimates. The method’s computational efficiency and its formal decomposition of uncertainty make it attractive for downstream tasks including out-of-distribution (OOD) detection, selective classification, and robust scientific modeling. However, recent analyses have revealed critical limitations in its epistemic quantification, which have driven ongoing theoretical and empirical refinements (Shen et al., 2024).

1. Second-Order Uncertainty Modeling in Deep Learning

The essential innovation of evidential uncertainty quantification is to regard the neural network output as parametrizing a “second-order” meta-distribution. In classification with $C$ classes, instead of a softmax producing $p_\theta(y|x) \in \Delta^{C-1}$, the network outputs an evidence vector $e(x) \in \mathbb{R}^C_{\ge 0}$, used to define Dirichlet parameters $\alpha(x) = e(x) + 1$. The resulting Dirichlet distribution $\operatorname{Dir}(\theta; \alpha(x))$ models a distribution over possible class-probability vectors $\theta \in \Delta^{C-1}$, explicitly capturing