Training-conditional coverage guarantees in conformal prediction concern the concentration of the error distribution, conditional on the training data, below some nominal level. The conformal prediction methodology has recently been generalized to the covariate shift setting, namely, the covariate distribution changes between the training and test data. In this paper, we study the training-conditional coverage properties of a range of conformal prediction methods under covariate shift via a weighted version of the Dvoretzky-Kiefer-Wolfowitz (DKW) inequality tailored for distribution change. The result for the split conformal method is almost assumption-free, while the results for the full conformal and jackknife+ methods rely on strong assumptions including the uniform stability of the training algorithm.

翻译：在共形预测中，训练条件覆盖性保证关注的是在给定训练数据条件下，误差分布低于某个名义水平的集中程度。共形预测方法最近已被推广到协变量偏移场景，即协变量分布在训练数据和测试数据之间发生变化。本文通过一种为分布变化定制的加权版Dvoretzky-Kiefer-Wolfowitz（DKW）不等式，研究了一系列共形预测方法在协变量偏移下的训练条件覆盖性质。分割共形方法的结果几乎是无需假设的，而全共形和刀切法+方法的结果则依赖于包括训练算法一致稳定性在内的强假设。