Uncertainty Estimation by Flexible Evidential Deep Learning

Uncertainty quantification (UQ) is crucial for deploying machine learning models in high-stakes applications, where overconfident predictions can lead to serious consequences. An effective UQ method must balance computational efficiency with the ability to generalize across diverse scenarios. Evidential deep learning (EDL) achieves efficiency by modeling uncertainty through the prediction of a Dirichlet distribution over class probabilities. However, the restrictive assumption of Dirichlet-distributed class probabilities limits EDL's robustness, particularly in complex or unforeseen situations. To address this, we propose *flexible evidential deep learning* ($\mathcal{F}$-EDL), which extends EDL by predicting a flexible Dirichlet distribution—a generalization of the Dirichlet distribution—over class probabilities. This approach provides a more expressive and adaptive representation of uncertainty, significantly enhancing UQ generalization and reliability under challenging scenarios. We theoretically establish several advantages of $\mathcal{F}$-EDL and empirically demonstrate its state-of-the-art UQ performance across diverse evaluation settings, including classical, long-tailed, and noisy in-distribution scenarios.