Epistemic Uncertainty is a measure of the lack of knowledge of a learner which diminishes with more evidence. While existing work focuses on using the variance of the Bayesian posterior due to parameter uncertainty as a measure of epistemic uncertainty, we argue that this does not capture the part of lack of knowledge induced by model misspecification. We discuss how the excess risk, which is the gap between the generalization error of a predictor and the Bayes predictor, is a sound measure of epistemic uncertainty which captures the effect of model misspecification. We thus propose a principled framework for directly estimating the excess risk by learning a secondary predictor for the generalization error and subtracting an estimate of aleatoric uncertainty, i.e., intrinsic unpredictability. We discuss the merits of this novel measure of epistemic uncertainty, and highlight how it differs from variance-based measures of epistemic uncertainty and addresses its major pitfall. Our framework, Direct Epistemic Uncertainty Prediction (DEUP) is particularly interesting in interactive learning environments, where the learner is allowed to acquire novel examples in each round. Through a wide set of experiments, we illustrate how existing methods in sequential model optimization can be improved with epistemic uncertainty estimates from DEUP, and how DEUP can be used to drive exploration in reinforcement learning. We also evaluate the quality of uncertainty estimates from DEUP for probabilistic image classification and predicting synergies of drug combinations.

翻译：认知不确定性是衡量学习者知识缺乏程度的指标，其会随着更多证据的积累而减少。现有研究通常将参数不确定性导致的贝叶斯后验方差作为认知不确定性的度量，但我们认为这并未捕捉模型误设所引发的知识缺乏部分。我们讨论了过风险（即预测器的泛化误差与贝叶斯预测器之间的差距）如何成为衡量认知不确定性的一种合理指标，该指标能够反映模型误设的影响。因此，我们提出了一种原则性框架，通过学习一个辅助预测器来直接估计泛化误差，并减去偶然不确定性（即内在的不可预测性）的估计值，从而直接估计过风险。我们探讨了这一新型认知不确定性度量的优点，并着重说明其与基于方差的认知不确定性度量的区别，以及如何解决后者的主要缺陷。我们的框架——直接认知不确定性预测（DEUP）在交互式学习环境中尤为有趣，因为学习者可以在每一轮中获取新的示例。通过一系列广泛的实验，我们展示了如何在序列模型优化中利用DEUP提供的认知不确定性估计改进现有方法，以及DEUP如何用于驱动强化学习中的探索。我们还评估了DEUP在概率图像分类及药物组合协同作用预测中不确定性估计的质量。