Vicinal Label Supervision for Reliable Aleatoric and Epistemic Uncertainty Estimation

Uncertainty estimation is crucial for ensuring the reliability of machine learning models in safety-critical applications. Evidential Deep Learning (EDL) offers a principled framework by modeling predictive uncertainty through Dirichlet distributions over class probabilities. However, existing EDL methods predominantly rely on level-0 hard labels, which supervise an uncertainty-aware model with full certainty. We argue that hard labels not only fail to capture epistemic uncertainty but also obscure the aleatoric uncertainty arising from inherent data noise and label ambiguity. As a result, EDL models often produce degenerate Dirichlet distributions that collapse to near-deterministic outputs. To overcome these limitations, we propose a vicinal risk minimization paradigm for EDL by incorporating level-1 supervision in the form of vicinally smoothed conditional label distributions. This richer supervision exposes the model to local label uncertainty, enhancing aleatoric uncertainty quantification while mitigating the degeneration of the Dirichlet distribution into a Dirac delta function, thereby improving epistemic uncertainty modeling. Extensive experiments show that our approach consistently outperforms standard EDL baselines across synthetic datasets, covariate-shifted out-of-distribution generalization tasks, out-of-distribution detection, and selective classification benchmarks, providing more reliable uncertainty estimates.