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We extend conformal prediction methodology beyond the case of exchangeabledata. In particular, we show that a weighted version of conformal predictioncan be used to compute distribution-free prediction intervals for problems inwhich the test and training covariate distributions differ, but the likelihoodratio between these two distributions is known---or, in practice, can beestimated accurately with access to a large set of unlabeled data (testcovariate points). Our weighted extension of conformal prediction also appliesmore generally, to settings in which the data satisfies a certain weightednotion of exchangeability. We discuss other potential applications of our newconformal methodology, including latent variable and missing data problems.

Conformal Prediction Under Covariate Shift