Evidential Deep Learning (EDL) is a popular framework for uncertainty-aware classification that models predictive uncertainty via Dirichlet distributions parameterized by neural networks. Despite its popularity, its theoretical foundations and behavior under distributional shift remain poorly understood. In this work, we provide a principled statistical interpretation by proving that EDL training corresponds to amortized variational inference in a hierarchical Bayesian model with a tempered pseudo-likelihood. This perspective reveals a major drawback: standard EDL conflates epistemic and aleatoric uncertainty, leading to systematic overconfidence on out-of-distribution (OOD) inputs. To address this, we introduce Density-Informed Pseudo-count EDL (DIP-EDL), a new parametrization that decouples class prediction from the magnitude of uncertainty by separately estimating the conditional label distribution and the marginal covariate density. This separation preserves evidence in high-density regions while shrinking predictions toward a uniform prior for OOD data. Theoretically, we prove that DIP-EDL achieves asymptotic concentration. Empirically, we show that our method enhances interpretability and improves robustness and uncertainty calibration under distributional shift.

翻译：证据深度学习（EDL）是一种流行的不确定性感知分类框架，它通过神经网络参数化的狄利克雷分布来建模预测不确定性。尽管EDL广受欢迎，但其理论基础以及在分布偏移下的行为仍鲜为人知。在本工作中，我们通过证明EDL训练对应于具有温度调节伪似然的层次贝叶斯模型中的摊销变分推断，从而提供了一个原则性的统计解释。这一视角揭示了一个主要缺陷：标准EDL将认知不确定性和偶然不确定性混为一谈，导致对分布外（OOD）输入的系统性过度自信。为解决此问题，我们引入了基于密度信息的伪计数证据深度学习（DIP-EDL），这是一种新的参数化方法，通过分别估计条件标签分布和边际协变量密度，将类别预测与不确定性大小解耦。这种分离保留了高密度区域的证据，同时使OOD数据的预测向均匀先验收缩。理论上，我们证明了DIP-EDL能够实现渐近集中性。实证上，我们表明该方法增强了可解释性，并提高了分布偏移下的鲁棒性和不确定性校准能力。