Some recent results for p-value free FDR Controls

Abstract

There has been significant interest among researchers in false discovery rate (FDR) control methods partially due to the strong desire from the scientific community for reproducibility and replicability of scientific discoveries. I will discuss our recent efforts trying to go beyond the recently popular p-value-free FDR control methods such as the knockoff filter (KF), data splitting (DS), and Gaussian mirror (GM). We present some power analysis of these methods under the weak-and-rare signal framework and discuss its implications under different correlation structures of the design matrix. We then focus on the DS procedure and its variant. In particular, we reformulate the DS method into a two-step procedure: using part of the data for estimation and feature ranking (in regression setting) and using the other part as checking/validation. FDR control can be achieved by monitoring how well the validation goes along the feature ranking. Under this setup, we may utilize external information and apply any procedure, such as a Bayesian method with spike-and-slab priors, to work on the first part of the data. We show that substantial power gain can be achieved in this way. The presentation is based on joint work with Buyu Lin, Tracy Ke, and Yuanchuan Guo.