Covariate Powered Cross-Weighted Multiple Testing

A fundamental task in the analysis of datasets with many variables is screening for associations. This can be cast as a multiple testing task, where objective achieving high detection power while controlling type I error. We consider $m$ hypothesis tests represented by pairs $((P_i, X_i))_{1\leq i \leq m}$ p-values $P_i$ and covariates $X_i$, such that $P_i \perp X_i$ if $H_i$ null. Here, we show how to use information potentially available about heterogeneities among hypotheses increase compared conventional procedures only $P_i$. To this end, upgrade existing weighted through Independent Hypothesis Weighting (IHW) framework data-driven weights are calculated function covariates. Finite sample guarantees, e.g., false discovery rate (FDR) control, derived from cross-weighting, data-splitting approach enables learning weight-covariate without overfitting long partitioned into independent folds, arbitrary within-fold dependence. IHW has increased methods do not covariate information. key implication rejection common setups should proceed according ranking p-values, but an alternative implied covariate-weighted p-values.