  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. This is because their validity
requires the deployment of symmetric 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 asymmetric rules and requires only
pairwise exchangeability 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 show improvements in power compared to
existing model-free methods in various scenarios.
