Model-free conditional independence feature screening for ultrahigh dimensional data

Lu Heng Wang, Jing Yuan Liu, Yong Li, Run Ze Li

Research output: Contribution to journalArticlepeer-review

3 Scopus citations

Abstract

Feature screening plays an important role in ultrahigh dimensional data analysis. This paper is concerned with conditional feature screening when one is interested in detecting the association between the response and ultrahigh dimensional predictors (e.g., genetic makers) given a low-dimensional exposure variable (such as clinical variables or environmental variables). To this end, we first propose a new index to measure conditional independence, and further develop a conditional screening procedure based on the newly proposed index. We systematically study the theoretical property of the proposed procedure and establish the sure screening and ranking consistency properties under some very mild conditions. The newly proposed screening procedure enjoys some appealing properties. (a) It is model-free in that its implementation does not require a specification on the model structure; (b) it is robust to heavy-tailed distributions or outliers in both directions of response and predictors; and (c) it can deal with both feature screening and the conditional screening in a unified way. We study the finite sample performance of the proposed procedure by Monte Carlo simulations and further illustrate the proposed method through two real data examples.

Original languageEnglish (US)
Pages (from-to)551-568
Number of pages18
JournalScience China Mathematics
Volume60
Issue number3
DOIs
StatePublished - Mar 1 2017

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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