SparseNet: coordinate descent with nonconvex penalties. (English) Zbl 1229.62091

Mazumder, Rahul; Friedman, Jerome H.; Hastie, Trevor

J. Am. Stat. Assoc. 106, No. 495, 1125-1138 (2011).

Summary: 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.

MSC:

62J05	Linear regression; mixed models
90C26	Nonconvex programming, global optimization
65C60	Computational problems in statistics (MSC2010)
90C90	Applications of mathematical programming

Keywords:

degrees of freedom; LASSO; nonconvex optimization; regularization surface; sparse regression; variable selection

Software:

sparsenet