Plug-in Losses for Evidential Deep Learning: A Simplified Framework for Uncertainty Estimation that Includes the Softmax Classifier
This work simplifies uncertainty estimation in deep learning for practitioners, but the contribution is incremental as it primarily provides theoretical justification and empirical validation of an approximation to existing EDL methods.
The authors propose a simplified framework for Evidential Deep Learning (EDL) by approximating the Dirichlet-based objective with a plug-in loss evaluated at the Dirichlet mean, showing that the approximation error decays with growing evidence. They validate their approach on the Google Speech Commands dataset, achieving comparable predictive accuracy and selective prediction performance to classical EDL while being simpler to implement.
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.