Trustworthy ML systems should not only return accurate predictions, but also a reliable representation of their uncertainty. Bayesian methods are commonly used to quantify both aleatoric and epistemic uncertainty, but alternative approaches, such as evidential deep learning methods, have become popular in recent years. The latter group of methods in essence extends empirical risk minimization (ERM) for predicting second-order probability distributions over outcomes, from which measures of epistemic (and aleatoric) uncertainty can be extracted. This paper presents novel theoretical insights of evidential deep learning, highlighting the difficulties in optimizing second-order loss functions and interpreting the resulting epistemic uncertainty measures. With a systematic setup that covers a wide range of approaches for classification, regression and counts, it provides novel insights into issues of identifiability and convergence in second-order loss minimization, and the relative (rather than absolute) nature of epistemic uncertainty measures.

翻译：可信赖的机器学习系统不仅应提供准确预测，还应具备可靠的不确定性表征能力。贝叶斯方法通常用于量化偶然不确定性和认知不确定性，但近年来证据深度学习等替代方法日益流行。后者本质上扩展了经验风险最小化（ERM）以预测输出上的二阶概率分布，从而可提取认知（及偶然）不确定性的度量。本文提出证据深度学习的新理论见解，揭示了优化二阶损失函数及解释所得认知不确定性度量的困难。通过涵盖分类、回归和计数等多种方法的系统性框架，本文为二阶损失最小化中的可辨识性与收敛性问题，以及认知不确定性度量的相对（而非绝对）本质提供了新洞见。