A Conformalized Empirical Bayes Method for Multiple Testing with Side Information

This article presents a Conformalized Locally Adaptive Weighting (CLAW) approach to multiple testing with side information. The proposed method employs innovative data-driven strategies to construct pairwise exchangeable scores, which are integrated into a generic algorithm that leverages a mirror process for controlling the false discovery rate (FDR). By combining principles from empirical Bayes with powerful techniques in conformal inference, CLAW provides a valid and efficient framework for incorporating structural information from both test data and auxiliary covariates. Unlike existing empirical Bayes FDR methods that primarily offer asymptotic validity, often under strong regularity conditions, CLAW controls the FDR in finite samples under weaker conditions. Extensive numerical studies using both simulated and real data demonstrate that CLAW exhibits superior performance compared to existing methods.