A Model-free Variable Screening Method Based on Leverage Score

Abstract

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.

Keywords:

• Bayesian information criteria
• General index model
• Leverage score
• Variable screening
• Singular value decomposition

Supplementary Material

The supplementary material provides the proof of Theorem 3.5, 3.10, 4.1, and 4.2, a detailed discussion of the implementation issues, and additional simulation studies.

Additional information

Funding

This work was supported by the U.S. National Science Foundation under grants DMS-1903226 and DMS-1925066, and the U.S. National Institute of Health under grant 5R01GM113242.