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June 2012 Sparsity with sign-coherent groups of variables via the cooperative-Lasso
Julien Chiquet, Yves Grandvalet, Camille Charbonnier
Ann. Appl. Stat. 6(2): 795-830 (June 2012). DOI: 10.1214/11-AOAS520


We consider the problems of estimation and selection of parameters endowed with a known group structure, when the groups are assumed to be sign-coherent, that is, gathering either nonnegative, nonpositive or null parameters. To tackle this problem, we propose the cooperative-Lasso penalty. We derive the optimality conditions defining the cooperative-Lasso estimate for generalized linear models, and propose an efficient active set algorithm suited to high-dimensional problems. We study the asymptotic consistency of the estimator in the linear regression setup and derive its irrepresentable conditions, which are milder than the ones of the group-Lasso regarding the matching of groups with the sparsity pattern of the true parameters. We also address the problem of model selection in linear regression by deriving an approximation of the degrees of freedom of the cooperative-Lasso estimator. Simulations comparing the proposed estimator to the group and sparse group-Lasso comply with our theoretical results, showing consistent improvements in support recovery for sign-coherent groups. We finally propose two examples illustrating the wide applicability of the cooperative-Lasso: first to the processing of ordinal variables, where the penalty acts as a monotonicity prior; second to the processing of genomic data, where the set of differentially expressed probes is enriched by incorporating all the probes of the microarray that are related to the corresponding genes.


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Julien Chiquet. Yves Grandvalet. Camille Charbonnier. "Sparsity with sign-coherent groups of variables via the cooperative-Lasso." Ann. Appl. Stat. 6 (2) 795 - 830, June 2012.


Published: June 2012
First available in Project Euclid: 11 June 2012

zbMATH: 1243.62101
MathSciNet: MR2976492
Digital Object Identifier: 10.1214/11-AOAS520

Keywords: continuous variables , grouped variables , microarray analysis , ordinal variables , Penalization , sign-coherence , Sparsity

Rights: Copyright © 2012 Institute of Mathematical Statistics


Vol.6 • No. 2 • June 2012
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