Covariate Information Number for Feature Screening in Ultrahigh-Dimensional Supervised Problems

Abstract

Contemporary high-throughput experimental and surveying techniques give rise to ultrahigh-dimensional supervised problems with sparse signals; that is, a limited number of observations (n), each with a very large number of covariates $(p\gg n)$, only a small share of which is truly associated with the response. In these settings, major concerns on computational burden, algorithmic stability, and statistical accuracy call for substantially reducing the feature space by eliminating redundant covariates before the use of any sophisticated statistical analysis. Along the lines of Pearson’s correlation coefficient-based sure independence screening and other model- and correlation-based feature screening methods, we propose a model-free procedure called covariate information number-sure independence screening (CIS). CIS uses a marginal utility connected to the notion of the traditional Fisher information, possesses the sure screening property, and is applicable to any type of response (features) with continuous features (response). Simulations and an application to transcriptomic data on rats reveal the comparative strengths of CIS over some popular feature screening methods. Supplementary materials for this article are available online.

Keywords:

• Affymetrix GeneChip Rat Genome 230 2.0 Array
• Fisher information
• Model-free
• Supervised problems
• Sure independence screening
• Ultrahigh dimension

Supplementary Materials and Codes

Proofs of theoretical results, full simulation results, details on the transcriptomic data application, and some relevant additional information are provided in an online Supplement. MATLAB (MATLAB 2020) and R (R Core Team 2020) source functions for the implementation of CIS and other feature screening procedures, codes for the numerical examples in the simulation study, and the analyses of the transcriptomic data are publicly available at the following link: bit.ly/CIS-Codes.

Acknowledgments

We thank Drs. Bharath Sriperumbudur, Amal Agarwal, and Mauricio Nascimento for helping with theoretical derivations; Dr. Weixin Yao for MATLAB codes to compute Covariate Information Matrices; Dr. Paolo Inglese for MATLAB code to compute distance correlations; and Drs. Xiaofeng Shao and Jingsi Zhang for R code to compute martingale difference correlations, the transcriptomic data, and R codes for its preprocessing. We also thank members of the Makova Lab at Penn State and Binglan (Victoria) Li for helping with the transcriptomic data application. Finally, we are grateful to the anonymous reviewers and the associate editor for crucial feedback that helped us greatly to improve our work.

Additional information

Funding

F. Chiaromonte and D. Nandy were supported by NSF grant DMS-1407639. R. Li was supported by NSF grants DMS-1820702, DMS-1953196, and DMS-2015539, and NIH grants R01CA229542, R01ES019672, and R21CA226300.