Uncertainty-aware machine learners, such as Bayesian neural networks, output a quantification of uncertainty instead of a point prediction. In this work, we provide uncertainty-aware learners with a principled framework to characterize, and identify ways to eliminate, errors that arise from reducible (epistemic) uncertainty. We introduce a principled definition of epistemic error, and provide a decompositional epistemic error bound which operates in the very general setting of imperfect multitask learning under distribution shift. In this setting, the training (source) data may arise from multiple tasks, the test (target) data may differ systematically from the source data tasks, and/or the learner may not arrive at an accurate characterization of the source data. Our bound separately attributes epistemic errors to each of multiple aspects of the learning procedure and environment. As corollaries of the general result, we provide epistemic error bounds specialized to the settings of Bayesian transfer learning and distribution shift within $\epsilon$-neighborhoods. We additionally leverage the terms in our bound to provide a novel definition of negative transfer.

翻译：不确定性感知机器学习模型，如贝叶斯神经网络，输出的是不确定性的量化而非点预测。本文为不确定性感知学习器提供了一个原则性框架，用以表征并识别由可约减（认知）不确定性引发的误差。我们提出了认知误差的原则性定义，并给出了一个分解式认知误差界，该误差界适用于分布漂移下不完美多任务学习这一非常一般的设定。在此设定中，训练（源）数据可能来自多个任务，测试（目标）数据可能与源数据任务存在系统性差异，且/或学习器可能无法准确刻画源数据的特征。我们的误差界将认知误差分别归因于学习过程与环境的多个方面。作为该一般性结果的推论，我们给出了专门针对贝叶斯迁移学习及$\epsilon$邻域内分布漂移两种场景的认知误差界。此外，我们利用误差界中的各项，提出了一种新颖的负迁移定义。