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Abstract:
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Conformal prediction has received tremendous attention in recent years with several applications across health and social sciences. Recently, conformal inference has offered new solutions to problems in causal inference, which has led to advances in modern discipline of semiparametric statistics for constructing novel, efficient prediction uncertainty quantification. We consider the problem of obtaining distribution-free prediction regions when there is a shift in the distribution of the covariates between the training and test data. We propose a method built on the efficient influence function for the average treatment effect among treated (ATT) functional that can be combined with any training algorithm. The prediction set attains nominal average coverage. This guaranty is a consequence of the product bias form of our proposal which implies correct coverage if either the propensity score or the conditional distribution of the response can be estimated sufficiently well, also known as double robustness. We also discuss parameter tuning for optimal performance, and resolve some open problems at the intersection of causal inference, semiparametric theory and conformal prediction.
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