  This paper proposes a model-free and data-adaptive feature screening method
for ultra-high dimensional datasets. 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 the data in the presence of heavy-tailed errors
and multivariate response. It enjoys both sure screening and rank consistency
properties under weak assumptions. Further, a two-step approach is proposed to
control the false discovery rate (FDR) in feature screening with the help of
knockoff features. It can be shown that the proposed two-step approach enjoys
both sure screening and FDR control if the pre-specified FDR level $\alpha$ is
greater or equal to $1/s$, where $s$ is the number of active features. The
superior empirical performance of the proposed methods is justified by various
numerical experiments and real data applications.
