Variational Inference for Evidential Deep Learning

2026-05-25

AI Summary

This work addresses critical limitations in traditional evidential deep learning, where the KL penalty suppresses evidence only for negative classes, leading to uncontrolled evidence growth and degraded uncertainty quantification, while the common choice of Dirichlet parameter α = e + 1 lacks theoretical justification. To overcome these issues, the authors reformulate evidential deep learning through variational inference, proposing the first VI-EDL framework. They derive an evidence lower bound (ELBO) that effectively regularizes evidence magnitude and establish a generalization error bound, rigorously proving that α = e + 1 minimizes this bound. The method achieves state-of-the-art performance on standard vision and medical datasets and demonstrates superior uncertainty quantification in out-of-distribution detection, noise identification, and autonomous driving tasks.

Abstract

While Deep Neural Networks (DNNs) achieve remarkable performance, their tendency to produce overconfident predictions. Evidential Deep Learning (EDL) mitigates this by formulating predictions as a Dirichlet distribution over class probabilities to explicitly quantify epistemic uncertainty. However, we found that the conventional EDL suffers from two fundamental limitations: a Kullback-Leibler (KL) penalty that only suppresses the evidence of negative classes, producing excessively high evidence therefore decreasing the model's ability to quantify uncertainty, and an absence in theoretical guarantee of setting Dirichlet parameter $α=e+1$. In this paper, we propose a mathematically principled framework, Variational Inference Evidential Deep Learning (VI-EDL). By reformulating evidential learning through the lens of variational inference, we derive an Evidence Lower Bound (ELBO), which prevents the evidence from growing excessively. Theoretically, we rigorously establish a generalization bound and reveal how the predicted uncertainty, feature and network complexity affect this bound, and why setting $\boldsymbolα = \mathbf{e} + \mathbf{1}$ can minimize it. Extensive experiments on standard visual and medical datasets demonstrate that VI-EDL achieves state-of-the-art performance, showing excellent performance in out-of-distribution detection, noise detection and autonomous driving scenario. The code is available in https://github.com/seutjw/VI-EDL.

Problem

• Evidential Deep Learning
• epistemic uncertainty
• Dirichlet distribution
• overconfident predictions
• Kullback-Leibler penalty

Innovation

• Variational Inference
• Evidential Deep Learning
• Uncertainty Quantification
• Dirichlet Distribution
• Generalization Bound