Generative conformal prediction under multiple covariate shifts

In this paper, we consider the problem of prediction inference for multiple target datasets under varying covariate shifts, a challenging scenario encountered in various economic and biomedical applications. We propose a two-step generative conformal prediction (GCP) method, which is efficient in handling imbalanced datasets. General results on the coverage validity of the proposed method are established, which elucidates the influence of the conditional generative learning procedure on the coverage validity. Furthermore, we prove the robustness of the proposed GCP intervals and provide theoretical evidence to demonstrate the advantages of our method over density ratio-based methods. Numerical studies, including simulation and real data examples, are conducted to compare the proposed method with existing density ratio-based approaches, to empirically illustrate the effectiveness of our method.