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

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

Software:

sparsenet
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