A Model-free Variable Screening Method Based on Leverage Score

• 成果类型: Article
• 署名作者: Zhong, Wenxuan; Liu, Yiwen; Zeng, Peng
• 署名单位: University System of Georgia; University of Georgia; University of Arizona; Auburn University System; Auburn University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1918554
• 发表日期: 2023
• 页码: 135-146
• 关键词: nonconcave penalized likelihood; Sliced Inverse Regression; gene-expression; selection; components; decompositions; algorithms; receptor

摘要

With rapid advances in information technology, massive datasets are collected in all fields of science, such as biology, chemistry, and social science. Useful or meaningful information is extracted from these data often through statistical learning or model fitting. In massive datasets, both sample size and number of predictors can be large, in which case conventional methods face computational challenges. Recently, an innovative and effective sampling scheme based on leverage scores via singular value decompositions has been proposed to select rows of a design matrix as a surrogate of the full data in linear regression. Analogously, variable screening can be viewed as selecting rows of the design matrix. However, effective variable selection along this line of thinking remains elusive. In this article, we bridge this gap to propose a weighted leverage variable screening method by using both the left and right singular vectors of the design matrix. We show theoretically and empirically that the predictors selected using our method can consistently include true predictors not only for linear models but also for complicated general index models. Extensive simulation studies show that the weighted leverage screening method is highly computationally efficient and effective. We also demonstrate its success in identifying carcinoma related genes using spatial transcriptome data.