Generative Conformal Prediction under Covariate Shift

Covariate shift is a common problem often encountered in supervised machine learning tasks, undermining the reliability of predictions when the training and target data distributions diverge. We propose a deep generative conformal prediction method for constructing dependable prediction intervals in the presence of covariate shift. The proposed approach involves the training of a conditional generator on source data, coupled with a novel deep neural estimation of the marginal density-ratio between source and target datasets. Our method facilitates the estimation of conditional quantiles and the computation of weighted conformity scores using a calibration set, thereby allowing for construction of tailored conformal prediction intervals for new inputs. Our contributions include the provision of theoretical guarantees for the nonasymptotic lower and upper validity coverage bounds and addressing the curse of dimensionality problem. Empirical validation through simulations and real-world datasets underscores the superiority of our proposed method over existing approaches.