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An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors

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  • She, Yiyuan

Abstract

High-dimensional data pose challenges in statistical learning and modeling. Sometimes the predictors can be naturally grouped where pursuing the between-group sparsity is desired. Collinearity may occur in real-world high-dimensional applications where the popular l1 technique suffers from both selection inconsistency and prediction inaccuracy. Moreover, the problems of interest often go beyond Gaussian models. To meet these challenges, nonconvex penalized generalized linear models with grouped predictors are investigated and a simple-to-implement algorithm is proposed for computation. A rigorous theoretical result guarantees its convergence and provides tight preliminary scaling. This framework allows for grouped predictors and nonconvex penalties, including the discrete l0 and the ‘l0+l2’ type penalties. Penalty design and parameter tuning for nonconvex penalties are examined. Applications of super-resolution spectrum estimation in signal processing and cancer classification with joint gene selection in bioinformatics show the performance improvement by nonconvex penalized estimation.

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  • She, Yiyuan, 2012. "An iterative algorithm for fitting nonconvex penalized generalized linear models with grouped predictors," Computational Statistics & Data Analysis, Elsevier, vol. 56(10), pages 2976-2990.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:10:p:2976-2990
    DOI: 10.1016/j.csda.2011.11.013
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    References listed on IDEAS

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    Cited by:

    1. Yong Wang & Guanglu Zhou & Xin Zhang & Wanquan Liu & Louis Caccetta, 2016. "The Non-convex Sparse Problem with Nonnegative Constraint for Signal Reconstruction," Journal of Optimization Theory and Applications, Springer, vol. 170(3), pages 1009-1025, September.
    2. Abdallah Mkhadri & Mohamed Ouhourane, 2015. "A group VISA algorithm for variable selection," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(1), pages 41-60, March.
    3. Yang, Hu & Yi, Danhui, 2015. "Studies of the adaptive network-constrained linear regression and its application," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 40-52.
    4. Lin, Yiqi & Song, Xinyuan, 2022. "Order selection for regression-based hidden Markov model," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    5. He Jiang, 2022. "A novel robust structural quadratic forecasting model and applications," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(6), pages 1156-1180, September.
    6. Mishra, Aditya & Dey, Dipak K. & Chen, Yong & Chen, Kun, 2021. "Generalized co-sparse factor regression," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    7. Wanling Xie & Hu Yang, 2023. "Group sparse recovery via group square-root elastic net and the iterative multivariate thresholding-based algorithm," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 469-507, September.
    8. Yiyuan She, 2017. "Selective factor extraction in high dimensions," Biometrika, Biometrika Trust, vol. 104(1), pages 97-110.

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