The false discovery rate for statistical pattern recognition

Abstract

The false discovery rate (FDR) and false nondiscovery rate (FNDR) have received considerable attention in the literature on multiple testing. These performance measures are also appropriate for classification, and in this work we develop generalization error analyses for FDR and FNDR when learning a classifier from labeled training data. Unlike more conventional classification performance measures, the empirical FDR and FNDR are not binomial random variables but rather a ratio of binomials, which introduces challenges not present in conventional formulations of the classification problem. We develop distribution-free uniform deviation bounds and apply these to obtain finite sample bounds and strong universal consistency. We also present a simulation study demonstrating the merits of variance-based bounds, which we also develop. In the context of multiple testing with FDR/FNDR, our framework may be viewed as a way to leverage training data to achieve distribution free, asymptotically optimal inference under the random effects model.