SparseNet: Coordinate Descent with Non-Convex Penalties

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SparseNet: Coordinate Descent with Non-Convex Penalties (2009)

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by Rahul Mazumder , Jerome Friedman , Trevor Hastie

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BibTeX

@MISC{Mazumder09sparsenet:coordinate,
    author = {Rahul Mazumder and Jerome Friedman and Trevor Hastie},
    title = {SparseNet: Coordinate Descent with Non-Convex Penalties},
    year = {2009}
}

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Abstract

We address the problem of sparse selection in linear models. A number of non-convex penalties have been proposed for this purpose, along with a variety of convex-relaxation algorithms for finding good solutions. In this paper we pursue the 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 (Zhang 2010) is ideally suited to this task, and we use it to demonstrate the performance of our algorithm. 1

Keyphrases

non-convex penalty coordinate descent mc penalty convergence property linear model good solution corresponding threshold function df-standardizing reparametrization coordinate-descent approach pathwise algorithm sparse selection convex-relaxation algorithm

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