Uncertainty Estimation by Flexible Evidential Deep Learning
Taeseong Yoon, Heeyoung Kim
TL;DR
Uncertainty Estimation by Flexible Evidential Deep Learning introduces $\mathcal{F}$-EDL, which extends Evidential Deep Learning by predicting a flexible Dirichlet distribution $FD^{K}(\alpha, p, \tau)$ over class probabilities to capture multimodal and input-dependent uncertainty. The approach derives a three-headed architecture that outputs $\alpha$, $p$, and $\tau$, with an objective that combines an expected MSE under $FD$ and a calibration term, enabling analytic training without sampling. Theoretical results establish conjugacy of the $FD$ prior, a Bayesian interpretation with input-dependent priors, and the reduction to standard EDL as a special case, along with multimodality and a mixture-decomposition of predictive uncertainty framed in a subjective-logic view. Empirically, $\mathcal{F}$-EDL achieves state-of-the-art UQ across classical, long-tailed, and noisy in-distribution settings and exhibits interpretable multimodal uncertainty and faithful epistemic behavior, while maintaining single-pass efficiency. The work positions $FD$-based uncertainty as a principled, scalable alternative to Dirichlet-only EDL for robust downstream uncertainty quantification.
Abstract
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 \textit{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.