On Exact Feature Screening in Ultrahigh-dimensional Binary Classification

In this article, we propose a new model-free feature screening method based on energy distances for ultrahigh-dimensional binary classification problems. Unlike existing methods, the cut-off involved in our procedure is data adaptive. With a high probability, the screened set retains only features after discarding all the noise variables. The proposed screening method is then extended to identify pairs of variables that are marginally undetectable, but have differences in their joint distributions. Finally, we build a classifier which maintains coherence between the proposed feature selection criteria and discrimination method, and also establish its risk consistency. An extensive numerical study with simulated data sets and real benchmark data sets show clear and convincing advantages of our classifier over what currently exists in the literature.