Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier

2026-05-21

AI Summary

This work addresses the computational complexity and implementation challenges associated with computing Dirichlet expectation targets in evidential deep learning (EDL). To overcome these issues, the authors propose a first-order empirical risk minimization approximation based on a plug-in loss evaluated at the Dirichlet mean, which substantially simplifies uncertainty modeling and training procedures. Notably, this approach is the first to formally incorporate standard softmax classifiers into the EDL theoretical framework and introduces a general strategy for plug-in loss approximation. Experiments on the Google Speech Commands dataset demonstrate that the proposed method achieves predictive accuracy and selective prediction performance comparable to classical EDL while significantly reducing implementation complexity. Furthermore, it enables, for the first time in speech recognition tasks, an EDL-driven analysis of the trade-off between coverage and accuracy.

Abstract

Real-world sensor-based learning systems require uncertainty estimation that is both reliable and computationally efficient. Evidential Deep Learning (EDL) provides single-pass uncertainty estimation by modeling the class probabilities via Dirichlet distributions, where the Dirichlet parameters are predicted by a learned neural network mapping. However, this approach can lead to computational challenges, as Dirichlet expected objectives are more complex than standard supervised learning losses, complicating their analysis and implementation. We address this issue by approximating the objective of the first-order empirical risk minimization problem induced by EDL with a plug-in loss evaluated at the Dirichlet mean and show that, under mild assumptions, the approximation error decays with growing evidence for a broad class of loss functions, including mean-squared error and cross-entropy loss. As a special case, our analysis provides justification for the use of softmax in the context of uncertainty estimation, since under a particular evidence-to-Dirichlet mapping, our framework includes the standard softmax classifier. We validate the proposed simplified objectives on the Google Speech Commands dataset and show that they achieve predictive accuracy and selective prediction performance comparable to classical EDL, while being simpler to implement using standard deep learning losses and training pipelines. To the best of our knowledge, this empirical analysis is the first to obtain coverage-accuracy trade-offs for speech recognition tasks through EDL.

Problem

• Evidential Deep Learning
• Uncertainty Estimation
• Dirichlet Distribution
• Plug-in Losses
• Softmax Classifier

Innovation

• Evidential Deep Learning
• Plug-in Loss
• Uncertainty Estimation
• Dirichlet Distribution
• Softmax Classifier