An important challenge facing modern machine learning is how to rigorously quantify the uncertainty of model predictions. Conveying uncertainty is especially important when there are changes to the underlying data distribution that might invalidate the predictive model. Yet, most existing uncertainty quantification algorithms break down in the presence of such shifts. We propose a novel approach that addresses this challenge by constructing \emph{probably approximately correct (PAC)} prediction sets in the presence of covariate shift. Our approach focuses on the setting where there is a covariate shift from the source distribution (where we have labeled training examples) to the target distribution (for which we want to quantify uncertainty). Our algorithm assumes given importance weights that encode how the probabilities of the training examples change under the covariate shift. In practice, importance weights typically need to be estimated; thus, we extend our algorithm to the setting where we are given confidence intervals for the importance weights rather than their true value. We demonstrate the effectiveness of our approach on various covariate shifts designed based on the DomainNet and ImageNet datasets.

论文提出了一种新的、能够在存在协变量转移情况下构建可能准确的预测集的方法，该方法重点关注源分布与目标分布之间的协变量转移，假设给定了编码训练样本概率变化的重要性权重，从而实现了不确定性的量化。

协变量偏移下的 PAC 预测集