Abstract
Conformal prediction has received tremendous attention in recent years and has offered new solutions to problems in missing data and causal inference; yet these advances have not leveraged modern semi-parametric efficiency theory for more efficient uncertainty quantification. We consider the problem of obtaining well-calibrated prediction regions that can data adaptively account for a shift in the distribution of covariates between training and test data. Under a covariate shift assumption analogous to the standard missing at random assumption, we propose a general framework based on efficient influence functions to construct well-calibrated prediction regions for the unobserved outcome in the test sample without compromising coverage.