A Generic Sure Independence Screening Procedure

ABSTRACT

Extracting important features from ultra-high dimensional data is one of the primary tasks in statistical learning, information theory, precision medicine, and biological discovery. Many of the sure independent screening methods developed to meet these needs are suitable for special models under some assumptions. With the availability of more data types and possible models, a model-free generic screening procedure with fewer and less restrictive assumptions is desirable. In this article, we propose a generic nonparametric sure independence screening procedure, called BCor-SIS, on the basis of a recently developed universal dependence measure: Ball correlation. We show that the proposed procedure has strong screening consistency even when the dimensionality is an exponential order of the sample size without imposing sub-exponential moment assumptions on the data. We investigate the flexibility of this procedure by considering three commonly encountered challenging settings in biological discovery or precision medicine: iterative BCor-SIS, interaction pursuit, and survival outcomes. We use simulation studies and real data analyses to illustrate the versatility and practicability of our BCor-SIS method. Supplementary materials for this article are available online.

Keywords:

• Ball correlation
• Rank
• Sure independence
• Variable screening

Additional information

Funding

Dr. Pan's research is partially supported by the National Natural Science Foundation of China (11701590), Natural Science Foundation of Guangdong Province of China (2017A030310053) and Young teacher program/Fundamental Research Funds for the Central Universities (17lgpy14). Dr. Wang's research is partially supported by the National Natural Science Foundation of China (11771462) and International Science & Technology Cooperation program of Guangdong (20163400042410001). Dr. Zhu's work was partially supported by the U.S. National Institutes of Health (Grant MH086633), the National Science Foundation (Grants SES-1357666 and DMS-1407655), a senior investigator grant from the Cancer Prevention Research Institute of Texas, and the endowed Bao-Shan Jing Professorship in Diagnostic Imaging. All authors contributed equally to this article.