R package SparseNet: coordinate descent with nonconvex penalties. We address the problem of sparse selection in linear models. A number of nonconvex penalties have been proposed in the literature for this purpose, along with a variety of convex-relaxation algorithms for finding good solutions. We pursue a coordinate-descent approach for optimization, and study its convergence properties. We characterize the properties of penalties suitable for this approach, study their corresponding threshold functions, and describe a df-standardizing reparametrization that assists our pathwise algorithm. The MC+ penalty is ideally suited to this task, and we use it to demonstrate the performance of our algorithm. Certain technical derivations and experiments related to this article are included in the supplementary materials section.

References in zbMATH (referenced in 71 articles , 1 standard article )

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  1. Hirose, Kei; Tateishi, Shohei; Konishi, Sadanori: Tuning parameter selection in sparse regression modeling (2013)
  2. Huang, Jian; Liu, Jin; Ma, Shuangge; Wang, Kai: Accounting for linkage disequilibrium in genome-wide association studies: a penalized regression method (2013)
  3. Hu, Jianwei; Chai, Hao: Adjusted regularized estimation in the accelerated failure time model with high dimensional covariates (2013)
  4. Strawderman, Robert L.; Wells, Martin T.; Schifano, Elizabeth D.: Hierarchical Bayes, maximum a posteriori estimators, and minimax concave penalized likelihood estimation (2013)
  5. Huang, Jian; Breheny, Patrick; Ma, Shuangge: A selective review of group selection in high-dimensional models (2012)
  6. Wen, Zaiwen; Goldfarb, Donald; Scheinberg, Katya: Block coordinate descent methods for semidefinite programming (2012)
  7. Zhang, Cun-Hui; Zhang, Tong: A general theory of concave regularization for high-dimensional sparse estimation problems (2012)
  8. Huang, Jian; Ma, Shuangge; Li, Hongzhe; Zhang, Cun-Hui: The sparse Laplacian shrinkage estimator for high-dimensional regression (2011)
  9. Mazumder, Rahul; Friedman, Jerome H.; Hastie, Trevor: SparseNet: coordinate descent with nonconvex penalties (2011)
  10. Yen, Tso-Jung: A majorization-minimization approach to variable selection using spike and slab priors (2011)
  11. Schifano, Elizabeth D.; Strawderman, Robert L.; Wells, Martin T.: Majorization-minimization algorithms for nonsmoothly penalized objective functions (2010)