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Proximal methods for the latent group lasso penalty

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  • Silvia Villa
  • Lorenzo Rosasco
  • Sofia Mosci
  • Alessandro Verri

Abstract

We consider a regularized least squares problem, with regularization by structured sparsity-inducing norms, which extend the usual ℓ 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. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Silvia Villa & Lorenzo Rosasco & Sofia Mosci & Alessandro Verri, 2014. "Proximal methods for the latent group lasso penalty," Computational Optimization and Applications, Springer, vol. 58(2), pages 381-407, June.
    • Handle: RePEc:spr:coopap:v:58:y:2014:i:2:p:381-407
    DOI: 10.1007/s10589-013-9628-6
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    References listed on IDEAS

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    1. Lukas Meier & Sara Van De Geer & Peter Bühlmann, 2008. "The group lasso for logistic regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(1), pages 53-71, February.
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    Cited by:

    1. Anastasis Kratsios & Cody B. Hyndman, 2017. "Non-Euclidean Conditional Expectation and Filtering," Papers 1710.05829, arXiv.org, revised Sep 2018.
    2. Dewei Zhang & Yin Liu & Sam Davanloo Tajbakhsh, 2022. "A First-Order Optimization Algorithm for Statistical Learning with Hierarchical Sparsity Structure," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 1126-1140, March.
    3. Christian Grussler & Pontus Giselsson, 2022. "Efficient Proximal Mapping Computation for Low-Rank Inducing Norms," Journal of Optimization Theory and Applications, Springer, vol. 192(1), pages 168-194, January.
    4. Du, Yu & Lin, Xiaodong & Pham, Minh & Ruszczyński, Andrzej, 2021. "Selective linearization for multi-block statistical learning," European Journal of Operational Research, Elsevier, vol. 293(1), pages 219-228.

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