Partial least squares regression with conditional orthogonal projection for variable selection

Abstract

Partial least squares regression (PLS) is a popular multivariate statistical analysis method. It not only can deal with high-dimensional variables but also can effectively select variables. However, the traditional PLS variable selection approaches cannot deal with some prior important variables. In this article, we propose two filter PLS variable selection algorithms (CPLS-BETA, CPLS-VIP) that combine with the prior variables by the conditional orthogonal projection. The performance of variable selection can be improved by projecting the other variables and response orthogonally on some prior active variables. Moreover, we introduce a kind of data-driven conditional method named forward projection PLS (FPPLS), which is suitable for the situation of unknown prior information. Finally, the validity of our method is verified by simulated datasets and real datasets.

Keywords:

• Forward projection
• Orthogonal projection
• Partial least squares regression
• Prior variables
• Variable selection

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China (Grant No. 12161042), China Postdoctoral Science Foundation funded project (Nos. 2019M662262, 2020M671961), Science Fund Project of Jiangxi Provincial Education Department [Nos. GJJ200522, GJJ200545], Science and technology research project of Education Department of Jiangxi Province (Grant No. GJJ210535), NSF of Jiangxi Province (No. 20192BAB201005), and Post-doctoral Science Foundation of Jiangxi Province (Nos. 2019KY47, 2021KY18).