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A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty

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  • Wentao Wang

    (School of Science, China University of Petroleum, Qingdao 266580, China)

  • Jiaxuan Liang

    (School of Science, China University of Petroleum, Qingdao 266580, China)

  • Rong Liu

    (School of Science, China University of Petroleum, Qingdao 266580, China)

  • Yunquan Song

    (School of Science, China University of Petroleum, Qingdao 266580, China)

  • Min Zhang

    (School of Science, China University of Petroleum, Qingdao 266580, China)

Abstract

Variable selection has been a hot topic, with various popular methods including lasso, SCAD, and elastic net. These penalized regression algorithms remain sensitive to noisy data. Furthermore, “concept drift” fundamentally distinguishes streaming data learning from batch learning. This article presents a method for noise-resistant regularization and variable selection in noisy data streams with multicollinearity, dubbed canal-adaptive elastic net, which is similar to elastic net and encourages grouping effects. In comparison to lasso, the canal adaptive elastic net is especially advantageous when the number of predictions ( p ) is significantly larger than the number of observations ( n ), and the data are multi-collinear. Numerous simulation experiments have confirmed that canal-adaptive elastic net has higher prediction accuracy than lasso, ridge regression, and elastic net in data with multicollinearity and noise.

Suggested Citation

  • Wentao Wang & Jiaxuan Liang & Rong Liu & Yunquan Song & Min Zhang, 2022. "A Robust Variable Selection Method for Sparse Online Regression via the Elastic Net Penalty," Mathematics, MDPI, vol. 10(16), pages 1-18, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2985-:d:892073
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    References listed on IDEAS

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    1. Yanming Li & Bin Nan & Ji Zhu, 2015. "Multivariate sparse group lasso for the multivariate multiple linear regression with an arbitrary group structure," Biometrics, The International Biometric Society, vol. 71(2), pages 354-363, June.
    2. 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.
    3. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    4. Shuang Xu & Chun-Xia Zhang, 2019. "Robust sparse regression by modeling noise as a mixture of gaussians," Journal of Applied Statistics, Taylor & Francis Journals, vol. 46(10), pages 1738-1755, July.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    7. Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
    8. 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.
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