False Discovery Rate Control For Structured Multiple Testing: Asymmetric Rules And Conformal <i>Q</i>-values

The effective utilization of structural information in data while ensuring statistical validity poses a significant challenge in false discovery rate (FDR) analyses. Conformal inference provides rigorous theory for grounding complex machine learning methods without relying on strong assumptions or highly idealized models. However, existing conformal methods have limitations in handling structured multiple testing, as their validity often requires the deployment of symmetric decision rules, which assume the exchangeability of data points and permutation-invariance of fitting algorithms. To overcome these limitations, we introduce the pseudo local index of significance (PLIS) procedure, which is capable of accommodating <i>asymmetric rules</i> and requires only <i>pairwise exchangeability</i> between the null conformity scores. We demonstrate that PLIS offers finite-sample guarantees in FDR control and the ability to assign higher weights to relevant data points. Numerical results confirm the effectiveness and robustness of PLIS and demonstrate improvements in power compared to existing model-free methods in various scenarios. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.