Journal of Guangxi Normal University(Natural Science Edition) ›› 2022, Vol. 40 ›› Issue (1): 43-56.doi: 10.16088/j.issn.1001-6600.2021060910

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High-dimensional Nonlinear Regression Model Based on JMI

ZHANG Zhifei1, DUAN Qian1, LIU Naijia2, HUANG Lei1*   

  1. 1. School of Mathematics, Southwest Jiaotong University, Chengdu Sichuan 611756, China;
    2. School of Statistics, Southwestern University of Finance and Economics, Chengdu Sichuan 611137, China
  • Received:2021-06-09 Revised:2021-06-27 Online:2022-01-25 Published:2022-01-24

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Abstract: Sure Independence Screening (SIS) has been widely used in the variable selection of linear regression models in ultra-high dimensional space, and extended to deal with the variable selection of generalized linear regression models. However, SIS cannot solve the problem of variable selection in nonlinear regression models well, and there are few existing studies on this problem. Therefore, how to effectively select variables in nonlinear regression models in ultra-high dimensional space becomes a problem with research value. Based on the classic SIS method, by considering Jackknife-based estimation of mutual information (JMI), a method combining SIS with JMI is proposed, and a specific algorithm is provided to realize the variable selection of the nonlinear regression model in the ultra-high dimensional space. Through some representative simulation experiments, this paper verifies the consistency of the proposed method. In addition, by the analysis of two examples gene data, the feasibility and practicality of the proposed method are elaborated.

Key words: ultra-high dimensional space, SIS, nonlinear regression, JMI, consistency

CLC Number: 

  • O212.1
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