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Group variable selection via group sparse neural network

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  • Zhang, Xin
  • Zhao, Junlong

Abstract

Group variable selection is an important issue in high-dimensional data modeling and most of existing methods consider only the linear model. Therefore, a new method based on the deep neural network (DNN), an increasingly popular nonlinear method in both statistics and deep learning communities, is proposed. The method is applicable to general nonlinear models, including the linear model as a special case. Specifically, a group sparse neural network (GSNN) is designed, where the definition of nonlinear group high-level features (NGHFs) is generalized to the network structure. A two-stage group sparse (TGS) algorithm is employed to induce group variables selection by performing group structure selection on the network. GSNN is promising for complex nonlinear systems with interactions and correlated predictors, overcoming the shortcomings of linear or marginal variable selection methods. Theoretical results on convergence and group-level selection consistency are also given. Simulations results and real data analysis demonstrate the superiority of our method.

Suggested Citation

  • Zhang, Xin & Zhao, Junlong, 2024. "Group variable selection via group sparse neural network," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    • Handle: RePEc:eee:csdana:v:192:y:2024:i:c:s0167947323002220
    DOI: 10.1016/j.csda.2023.107911
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    References listed on IDEAS

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    1. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    2. Christina Curtis & Sohrab P. Shah & Suet-Feung Chin & Gulisa Turashvili & Oscar M. Rueda & Mark J. Dunning & Doug Speed & Andy G. Lynch & Shamith Samarajiwa & Yinyin Yuan & Stefan Gräf & Gavin Ha & Gh, 2012. "The genomic and transcriptomic architecture of 2,000 breast tumours reveals novel subgroups," Nature, Nature, vol. 486(7403), pages 346-352, June.
    3. Faming Liang & Qizhai Li & Lei Zhou, 2018. "Bayesian Neural Networks for Selection of Drug Sensitive Genes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(523), pages 955-972, July.
    4. Patrick Breheny, 2015. "The group exponential lasso for bi‐level variable selection," Biometrics, The International Biometric Society, vol. 71(3), pages 731-740, September.
    5. Fan, Jianqing & Feng, Yang & Song, Rui, 2011. "Nonparametric Independence Screening in Sparse Ultra-High-Dimensional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 544-557.
    6. Hengjian Cui & Runze Li & Wei Zhong, 2015. "Model-Free Feature Screening for Ultrahigh Dimensional Discriminant Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 630-641, June.
    7. Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    8. Jian Huang & Shuange Ma & Huiliang Xie & Cun-Hui Zhang, 2009. "A group bridge approach for variable selection," Biometrika, Biometrika Trust, vol. 96(2), pages 339-355.
    9. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    10. Ming Yuan & Yi Lin, 2006. "Model selection and estimation in regression with grouped variables," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(1), pages 49-67, February.
    11. Yanyuan Ma & Liping Zhu, 2013. "A Review on Dimension Reduction," International Statistical Review, International Statistical Institute, vol. 81(1), pages 134-150, April.
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