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Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space

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  • Shan Luo
  • Zehua Chen

Abstract

In this article, we propose a method called sequential Lasso (SLasso) for feature selection in sparse high-dimensional linear models. The SLasso selects features by sequentially solving partially penalized least squares problems where the features selected in earlier steps are not penalized. The SLasso uses extended BIC (EBIC) as the stopping rule. The procedure stops when EBIC reaches a minimum. The asymptotic properties of SLasso are considered when the dimension of the feature space is ultra high and the number of relevant feature diverges. We show that, with probability converging to 1, the SLasso first selects all the relevant features before any irrelevant features can be selected, and that the EBIC decreases until it attains the minimum at the model consisting of exactly all the relevant features and then begins to increase. These results establish the selection consistency of SLasso. The SLasso estimators of the final model are ordinary least squares estimators. The selection consistency implies the oracle property of SLasso. The asymptotic distribution of the SLasso estimators with diverging number of relevant features is provided. The SLasso is compared with other methods by simulation studies, which demonstrates that SLasso is a desirable approach having an edge over the other methods. The SLasso together with the other methods are applied to a microarray data for mapping disease genes. Supplementary materials for this article are available online.

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  • Shan Luo & Zehua Chen, 2014. "Sequential Lasso Cum EBIC for Feature Selection With Ultra-High Dimensional Feature Space," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1229-1240, September.
    • Handle: RePEc:taf:jnlasa:v:109:y:2014:i:507:p:1229-1240
    DOI: 10.1080/01621459.2013.877275
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    References listed on IDEAS

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    Cited by:

    1. Shan Luo, 2020. "Variable selection in high-dimensional sparse multiresponse linear regression models," Statistical Papers, Springer, vol. 61(3), pages 1245-1267, June.
    2. Liu, Jianyu & Yu, Guan & Liu, Yufeng, 2019. "Graph-based sparse linear discriminant analysis for high-dimensional classification," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 250-269.
    3. Yawei He & Zehua Chen, 2016. "The EBIC and a sequential procedure for feature selection in interactive linear models with high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(1), pages 155-180, February.
    4. Eun Ryung Lee & Seyoung Park & Sang Kyu Lee & Hyokyoung G. Hong, 2023. "Quantile forward regression for high-dimensional survival data," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 29(4), pages 769-806, October.
    5. Hong, Hyokyoung G. & Zheng, Qi & Li, Yi, 2019. "Forward regression for Cox models with high-dimensional covariates," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 268-290.
    6. Yuyang Liu & Pengfei Pi & Shan Luo, 2023. "A semi-parametric approach to feature selection in high-dimensional linear regression models," Computational Statistics, Springer, vol. 38(2), pages 979-1000, June.
    7. Li, Peili & Jiao, Yuling & Lu, Xiliang & Kang, Lican, 2022. "A data-driven line search rule for support recovery in high-dimensional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    8. Jian Huang & Yuling Jiao & Lican Kang & Jin Liu & Yanyan Liu & Xiliang Lu, 2022. "GSDAR: a fast Newton algorithm for $$\ell _0$$ ℓ 0 regularized generalized linear models with statistical guarantee," Computational Statistics, Springer, vol. 37(1), pages 507-533, March.
    9. Zehua Chen & Yiwei Jiang, 2020. "A two-stage sequential conditional selection approach to sparse high-dimensional multivariate regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(1), pages 65-90, February.
    10. Honda, Toshio & 本田, 敏雄 & Lin, Chien-Tong, 2022. "Forward variable selection for ultra-high dimensional quantile regression models," Discussion Papers 2021-02, Graduate School of Economics, Hitotsubashi University.
    11. Peili Li & Min Liu & Zhou Yu, 2023. "A global two-stage algorithm for non-convex penalized high-dimensional linear regression problems," Computational Statistics, Springer, vol. 38(2), pages 871-898, June.
    12. Ke Yu & Shan Luo, 2022. "A sequential feature selection procedure for high-dimensional Cox proportional hazards model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 74(6), pages 1109-1142, December.
    13. Luo, Shan & Chen, Zehua, 2020. "A procedure of linear discrimination analysis with detected sparsity structure for high-dimensional multi-class classification," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    14. Toshio Honda & Chien-Tong Lin, 2023. "Forward variable selection for ultra-high dimensional quantile regression models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 75(3), pages 393-424, June.
    15. Akira Shinkyu, 2023. "Forward Selection for Feature Screening and Structure Identification in Varying Coefficient Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 485-511, February.

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