基于Jackknife互信息的高维非线性回归模型研究

doi:10.16088/j.issn.1001-6600.2021060910

广西师范大学学报（自然科学版） ›› 2022, Vol. 40 ›› Issue (1): 43-56.doi: 10.16088/j.issn.1001-6600.2021060910

基于Jackknife互信息的高维非线性回归模型研究

张治飞¹, 段谦¹, 刘乃嘉², 黄磊^1*

1.西南交通大学数学学院, 四川成都 611756;
2.西南财经大学统计学院, 四川成都 611137

收稿日期:2021-06-09 修回日期:2021-06-27 出版日期:2022-01-25 发布日期:2022-01-24
通讯作者: 黄磊(1987—), 男, 四川成都人, 西南交通大学副教授。 E-mail: stahl@swjtu.edu.cn
基金资助:
国家自然科学基金重点项目(72033002); 国家自然科学基金(11771066)

High-dimensional Nonlinear Regression Model Based on JMI

ZHANG Zhifei¹, DUAN Qian¹, LIU Naijia², HUANG Lei^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

摘要/Abstract

摘要： 确定独立筛选(SIS)方法在处理超高维稀疏线性回归模型的变量选择问题上已得到了广泛的应用,且已被推广到处理广义线性回归模型的变量选择问题。但SIS不能很好地解决非线性回归模型的变量选择问题,关于该问题的现有研究也较少,因此,如何有效地对超高维稀疏非线性回归模型进行变量选择是一个具有研究价值的问题。本文在经典的SIS方法基础上,利用互信息的刀切估计(JMI),提出JMI与SIS相结合的方法,给出具体算法步骤,以实现超高维稀疏非线性回归模型的变量选择问题,并通过一些有代表性的统计模拟试验,验证所提方法的相合性,同时通过2个超高维基因数据的实例分析,对所提方法的可行性以及实用性进行说明。

关键词: 超高维空间, SIS, 非线性回归, JMI, 相合性

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

中图分类号:

O212.1

张治飞, 段谦, 刘乃嘉, 黄磊. 基于Jackknife互信息的高维非线性回归模型研究[J]. 广西师范大学学报（自然科学版）, 2022, 40(1): 43-56.

ZHANG Zhifei, DUAN Qian, LIU Naijia, HUANG Lei. High-dimensional Nonlinear Regression Model Based on JMI[J]. Journal of Guangxi Normal University(Natural Science Edition), 2022, 40(1): 43-56.

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基于Jackknife互信息的高维非线性回归模型研究

High-dimensional Nonlinear Regression Model Based on JMI

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