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 80 articles , 1 standard article )

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  1. Piotr Pokarowski, Wojciech Rejchel, Agnieszka Soltys, Michal Frej, Jan Mielniczuk: Improving Lasso for model selection and prediction (2019) arXiv
  2. Shi, Yueyong; Xu, Deyi; Cao, Yongxiu; Jiao, Yuling: Variable selection via generalized SELO-penalized Cox regression models (2019)
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  4. Adachi, Kohei; Trendafilov, Nickolay T.: Sparsest factor analysis for clustering variables: a matrix decomposition approach (2018)
  5. Choiruddin, Achmad; Coeurjolly, Jean-François; Letué, Frédérique: Convex and non-convex regularization methods for spatial point processes intensity estimation (2018)
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  7. Huang, Jian; Jiao, Yuling; Liu, Yanyan; Lu, Xiliang: A constructive approach to (L_0) penalized regression (2018)
  8. Jin, Shaobo; Moustaki, Irini; Yang-Wallentin, Fan: Approximated penalized maximum likelihood for exploratory factor analysis: an orthogonal case (2018)
  9. Li, Xingguo; Zhao, Tuo; Arora, Raman; Liu, Han; Hong, Mingyi: On faster convergence of cyclic block coordinate descent-type methods for strongly convex minimization (2018)
  10. Ročková, Veronika; George, Edward I.: The spike-and-slab LASSO (2018)
  11. Shi, Yue-Yong; Cao, Yong-Xiu; Yu, Ji-Chang; Jiao, Yu-Ling: Variable selection via generalized SELO-penalized linear regression models (2018)
  12. Shi, Yue Yong; Jiao, Yu Ling; Cao, Yong Xiu; Liu, Yan Yan: An alternating direction method of multipliers for MCP-penalized regression with high-dimensional data (2018)
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  20. Giuzio, Margherita: Genetic algorithm versus classical methods in sparse index tracking (2017)