Feature Screening for High-Dimensional Variable Selection in Generalized Linear Models.

The two-stage feature screening method for linear models applies dimension reduction at first stage to screen out nuisance features and dramatically reduce the dimension to a moderate size; at the second stage, penalized methods such as LASSO and SCAD could be applied for feature selection. A majority of subsequent works on the sure independent screening methods have focused mainly on the linear model. This motivates us to extend the independence screening method to generalized linear models, and particularly with binary response by using the point-biserial correlation. We develop a two-stage feature screening method called point-biserial sure independence screening (PB-SIS) for high-dimensional generalized linear models, aiming for high selection accuracy and low computational cost. We demonstrate that PB-SIS is a feature screening method with high efficiency. The PB-SIS method possesses the sure independence property under certain regularity conditions. A set of simulation studies are conducted and confirm the sure independence property and the accuracy and efficiency of PB-SIS. Finally we apply PB-SIS to one real data example to show its effectiveness.