Model-Free Feature Screening and FDR Control With Knockoff Features

Abstract

This article proposes a model-free and data-adaptive feature screening method for ultrahigh-dimensional data. The proposed method is based on the projection correlation which measures the dependence between two random vectors. This projection correlation based method does not require specifying a regression model, and applies to data in the presence of heavy tails and multivariate responses. It enjoys both sure screening and rank consistency properties under weak assumptions. A two-step approach, with the help of knockoff features, is advocated to specify the threshold for feature screening such that the false discovery rate (FDR) is controlled under a prespecified level. The proposed two-step approach enjoys both sure screening and FDR control simultaneously if the prespecified FDR level is greater or equal to 1/s, where s is the number of active features. The superior empirical performance of the proposed method is illustrated by simulation examples and real data applications. Supplementary materials for this article are available online.