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
[1] 张晓琴, 刘莉楠. 基于亲密度和吸引力的二分网络社区发现算法[J]. 计算机工程与应用, 2019, 55(23): 170-176. DOI: 10.3778/j.issn.1002-8331.1808-0090.
[2]韦春荣, 何楚. 基于改进型互信息的遥感图像配准方法[J]. 广西师范大学学报(自然科学版), 2014, 32(2): 20-25. DOI: 10.16088/j.issn.1001-6600.2014.02.033.
[3]ZENG X L, XIA Y C, TONG H. Jackknife approach to the estimation of mutual information[J]. Proceedings of the National Academy of Sciences of the United States of America, 2018, 115(40): 9956-9961. DOI: 10.1073/pnas.1715593115.
[4]DESBOULETS L D D. A review on variable selection in regression analysis[J]. Econometrics, 2018, 6(4): 45. DOI: 10.3390/econometrics6040045.
[5]FAN J Q, LV J C. Sure independence screening for ultrahigh dimensional feature space[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2008, 70(5): 849-911. DOI:10.1111/j.1467-9868.2008.00674.x.
[6]张秀秀. 基于(I)SIS的变量选择方法及其在极高维数据生存分析中的应用[D]. 太原: 山西医科大学, 2013. DOI: 10.7666/d.Y2339335.
[7]马学俊. GSIS超高维变量选择[J]. 统计与信息论坛, 2015, 30(8): 16-19. DOI: 10.3969/j.issn.1007-3116.2015.08.004.
[8]HALL P, MILLER H. Using generalized correlation to effect variable selection in very high dimensional problems[J]. Journal of Computational and Graphical Statistics, 2009, 18(3): 533-550. DOI: 10.1198/jcgs.2009.08041.
[9]ANTONIADIS A, FAN J Q. Regularization of wavelet approximations[J]. Journal of the American Statistical Association, 2001, 96(455): 939-967. DOI: 10.1198/016214501753208942.
[10]YUAN M, LIN Y. Model selection and estimation in regression with grouped variables[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2006, 68(1): 49-67. DOI: 10.1111/j.1467-9868.2005.00532.x.
[11]LIN Y, ZHANG H H. Component selection and smoothing in multivariate nonparametric regression[J]. The Annals of Statistics, 2006, 34(5): 2272-2297. DOI: 10.1214/009053606000000722.
[12]RAVIKUMAR P, LAFFERTY J, LIU H, et al. Sparse additive models[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology, 2009, 71(5): 1009-1030. DOI: 10.1111/j.1467-9868.2009.00718.x.
[13]ZHU L P, LI L X, LI R Z, et al. Model-free feature screening for ultrahigh dimensional data[J]. Journal of the American Statistical Association, 2011, 106(496): 1464-1475. DOI: 10.1198/jasa.2011.tm10563.
[14]CUI H J, LI R Z, ZHONG W. Model-free feature screening for ultrahigh dimensional discriminant analysis[J]. Journal of the American Statistical Association, 2015, 110(510): 630-641. DOI: 10.1080/01621459.2014.920256.
[15]MAI Q, ZOU H. The Kolmogorov filter for variable screening in high-dimensional binary classification[J]. Biometrika, 2013, 100(1): 229-234. DOI: 10.1093/biomet/ass062.
[16]WU S, XUE H Q, WU Y C, et al. Variable selection for sparse high-dimensional nonlinear regression models by combining nonnegative garrote and sure independence screening[J]. Statistica Sinica, 2014, 24(3): 1365-1387. DOI: 10.5705/ss.2012.316.
[17]DAVIDSON R, MACKINNON J G, et al. Implicit alternatives and the local power of test statistics[J]. Econometrica, 1987, 55(6): 1305-1329. DOI: 10.2307/1913558.
[18]GOLUB T R, SLONIM D K, TAMAYO P, et al. Molecular classification of cancer: class discovery and class prediction by gene expression monitoring[J]. Science, 1999, 286(5439): 531-537. DOI: 10.1126/science.286.5439.531.
[19]RABANI M, LEVIN J Z, FAN L, et al. Metabolic labeling of RNA uncovers principles of RNA production and degradation dynamics in mammalian cells[J]. Nature Biotechnology, 2011, 29(5): 436-442. DOI: 10.1038/nbt.1861.
[20]YANG Y, ZHANG T, ZOU H. Flexible expectile regression in reproducing kernel Hilbert spaces[J]. Technometrics, 2018, 60(1): 26-35. DOI: 10.1080/00401706.2017.1291450.
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