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

Listed author(s):
  • She, Yiyuan
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    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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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 10 ()
    Pages: 2976-2990

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    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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    1. Jiahua Chen & Zehua Chen, 2008. "Extended Bayesian information criteria for model selection with large model spaces," Biometrika, Biometrika Trust, vol. 95(3), pages 759-771.
    2. She, Yiyuan & Owen, Art B., 2011. "Outlier Detection Using Nonconvex Penalized Regression," Journal of the American Statistical Association, American Statistical Association, vol. 106(494), pages 626-639.
    3. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    4. Efron, Bradley, 2009. "Empirical Bayes Estimates for Large-Scale Prediction Problems," Journal of the American Statistical Association, American Statistical Association, vol. 104(487), pages 1015-1028.
    5. 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.
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