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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.

Suggested Citation

  • 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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    6. 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.
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    Cited by:

    1. repec:spr:joptap:v:170:y:2016:i:3:d:10.1007_s10957-016-0869-2 is not listed on IDEAS
    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. repec:oup:biomet:v:104:y:2017:i:1:p:97-110. is not listed on IDEAS

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