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

作　　者：张治飞 段谦 刘乃嘉 黄磊[1] ZHANG Zhifei;DUAN Qian;LIU Naijia;HUANG Lei(School of Mathematics,Southwest Jiaotong University,Chengdu Sichuan 611756,China;School of Statistics,Southwestern University of Finance and Economics,Chengdu Sichuan 611137,China)

机构地区：[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

出　　处：《广西师范大学学报（自然科学版）》2022年第1期43-56,共14页Journal of Guangxi Normal University:Natural Science Edition

基　　金：国家自然科学基金重点项目(72033002);国家自然科学基金(11771066)。

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。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.

关 键 词：超高维空间 SIS 非线性回归 JMI 相合性 

分 类 号：O212.1[理学—概率论与数理统计] Q811.4[理学—数学]