Georgia Institute of Technology College of Sciences

This paper proposes a model-free and data-adaptive feature screening method for ultra-high 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 pre-specified level. The proposed two-step approach enjoys both sure screening and FDR control simultaneously if the pre-specified 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. This is a joint work with Wanjun Liu, Jingyuan Liu and Runze Li.