Proximal methods for the latent group lasso penalty
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Author(s)
Villa, Silvia
Rosasco, Lorenzo Andrea
Mosci, Sofia
Verri, Alessandro
Date Issued
December 2013
Journal
Computational Optimization and Applications
Publisher
Springer US
Citation
Villa, Silvia, Lorenzo Rosasco, Sofia Mosci, and Alessandro Verri. “Proximal Methods for the Latent Group Lasso Penalty.” Comput Optim Appl 58, no. 2 (December 21, 2013): 381–407.
Version
Author's final manuscript
Abstract
We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual ℓ[subscript 1] and the group lasso penalty, by allowing the subsets to overlap. Such regularizations lead to nonsmooth problems that are difficult to optimize, and we propose in this paper a suitable version of an accelerated proximal method to solve them. We prove convergence of a nested procedure, obtained composing an accelerated proximal method with an inner algorithm for computing the proximity operator. By exploiting the geometrical properties of the penalty, we devise a new active set strategy, thanks to which the inner iteration is relatively fast, thus guaranteeing good computational performances of the overall algorithm. Our approach allows to deal with high dimensional problems without pre-processing for dimensionality reduction, leading to better computational and prediction performances with respect to the state-of-the art methods, as shown empirically both on toy and real data.
MIT Department
Massachusetts Institute of Technology. Department of Brain and Cognitive Sciences
McGovern Institute for Brain Research at MIT
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Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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DOI of Published Version
https://doi.org/10.1007/s10589-013-9628-6
