Abstract

We consider feature screening for high-dimensional response data without and

with the existence of confounding factors. First, we introduce kernel covariance

and kernel correlation for high-dimensional associaiton analysis, and further propose partial kernel covariance and partial kernel correlation that can handle situa-

tions with confounding factors. Then, based on the kernel correlation and partial

kernel correlation, we propose two feature screening procedures. Both screening

procedures possess sure screening property and ranking consistency property, and

are complementary to each other by respectively dealing with situations without

and with the existence of confounding factors. The proposed procedures make no

assumptions on model, and are suitable for high-dimensional response variable

and non-Euclidean data. Extensive simulation results and a real data analysis

demonstrate the satisfying performances and advantages of the proposed procedures over existing methods.

Information

Preprint No.SS-2023-0290
Manuscript IDSS-2023-0290
Complete AuthorsYuke Shi, Na Li, Qizhai Li, Dongdong Pan, Jinjuan Wang
Corresponding AuthorsJinjuan Wang
Emailswangjinjuan@bit.edu.cn

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Acknowledgments

We would like to express our sincere gratitude to Qunqiang Feng for his invaluable contributions to this article. Jinjuan Wang has been supported by

National Natural Science Foundation of China (NSFC) (Grant No. 12101047)

and Beijing Institute of Technology Research Fund Program for Young

Scholars. Qizhai Li has been supported by National Natural Science Foundation of China (NSFC) (Grant No. 12325110) and CAS Project for Young

Scientists in Basic Research (Grant No. YSBR-034).

Supplementary Materials

The proofs of Theorems 1 and 2, as well as additional numerical simulations

on one-dimensional response variable models, two distinct kernels, and other

popular machine learning approaches, can be found in the Supplementary

Material.

Supplementary materials are available for download.