Sure Independence Screening

Big data is ubiquitous in various fields of sciences, engineering, medicine, social sciences, and humanities. It is often accompanied by a large number of variables and features. While adding much greater flexibility to modeling with enriched feature space, ultra-high dimensional data analysis poses fundamental challenges to scalable learning and inference with good statistical efficiency. Sure independence screening is a simple and effective method to this endeavor. This framework of two-scale statistical learning, consisting of large-scale screening followed by moderate-scale variable selection introduced in Fan and Lv (2008), has been extensively investigated and extended to various model settings ranging from parametric to semiparametric and nonparametric for regression, classification, and survival analysis. This article provides an overview on the developments of sure independence screening over the past decade. These developments demonstrate the wide applicability of the sure independence screening based learning and inference for big data analysis with desired scalability and theoretical guarantees.