Variable Selection and Feature Screening

This chapter provides a selective review on feature screening methods for ultra-high dimensional data. The main idea of feature screening is reducing the ultra-high dimensionality of the feature space to a moderate size in a fast and efficient way and meanwhile retaining all the important features in the reduced feature space. This is referred to as the sure screening property. After feature screening, more sophisticated methods can be applied to reduced feature space for further analysis such as parameter estimation and statistical inference. This chapter only focuses on the feature screening stage. From the perspective of different types of data, we review feature screening methods for independent and identically distributed data, longitudinal data, and survival data. From the perspective of modeling, we review various models including linear model, generalized linear model, additive model, varying-coefficient model, Cox model, etc. We also cover some model-free feature screening procedures.