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. He, Qianchuan; Kong, Linglong; Wang, Yanhua; Wang, Sijian; Chan, Timothy A.; Holland, Eric: Regularized quantile regression under heterogeneous sparsity with application to quantitative genetic traits (2016)
  2. Liu, Hongcheng; Yao, Tao; Li, Runze: Global solutions to folded concave penalized nonconvex learning (2016)
  3. Liu, Zhenqiu; Li, Gang: Efficient regularized regression with (L_0) penalty for variable selection and network construction (2016)
  4. Zhang, Xiang; Wu, Yichao; Wang, Lan; Li, Runze: A consistent information criterion for support vector machines in diverging model spaces (2016)
  5. Aragam, Bryon; Zhou, Qing: Concave penalized estimation of sparse Gaussian Bayesian networks (2015)
  6. Hirose, Kei; Yamamoto, Michio: Sparse estimation via nonconcave penalized likelihood in factor analysis model (2015)
  7. Loh, Po-Ling; Wainwright, Martin J.: Regularized (M)-estimators with nonconvexity: statistical and algorithmic theory for local optima (2015)
  8. Pan, Zheng; Zhang, Changshui: Relaxed sparse eigenvalue conditions for sparse estimation via non-convex regularized regression (2015)
  9. Wright, Stephen J.: Coordinate descent algorithms (2015)
  10. Xiang, Shuo; Shen, Xiaotong; Ye, Jieping: Efficient nonconvex sparse group feature selection via continuous and discrete optimization (2015)
  11. Zhang, Zhihua; Li, Jin: Compound Poisson processes, latent shrinkage priors and Bayesian nonconvex penalization (2015)
  12. Chu, Ge-Jin; Liang, Yong; Wang, Jia-Xuan: Novel harmonic regularization approach for variable selection in Cox’s proportional hazards model (2014)
  13. Fan, Jianqing; Xue, Lingzhou; Zou, Hui: Strong oracle optimality of folded concave penalized estimation (2014)
  14. Hirose, Kei; Yamamoto, Michio: Estimation of an oblique structure via penalized likelihood factor analysis (2014)
  15. Jiang, Dingfeng; Huang, Jian: Majorization minimization by coordinate descent for concave penalized generalized linear models (2014)
  16. Kappen, Hilbert J.; Gómez, Vicenç: The variational Garrote (2014)
  17. Marchetti, Yuliya; Zhou, Qing: Solution path clustering with adaptive concave penalty (2014)
  18. Shi, Yue-Yong; Cao, Yong-Xiu; Jiao, Yu-Ling; Liu, Yan-Yan: SICA for Cox’s proportional hazards model with a diverging number of parameters (2014)
  19. Wang, Zhaoran; Liu, Han; Zhang, Tong: Optimal computational and statistical rates of convergence for sparse nonconvex learning problems (2014)
  20. Yen, Yu-Min; Yen, Tso-Jung: Solving norm constrained portfolio optimization via coordinate-wise descent algorithms (2014)