Training-Conditional Coverage Bounds under Covariate Shift

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.