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A random block-coordinate Douglas–Rachford splitting method with low computational complexity for binary logistic regression

Author

Listed:
  • Luis M. Briceño-Arias

    (Universidad Técnica Federico Santa María)

  • Giovanni Chierchia

    (Université Paris-Est (UPEM))

  • Emilie Chouzenoux

    (Université Paris-Est (UPEM)
    University Paris-Saclay)

  • Jean-Christophe Pesquet

    (University Paris-Saclay)

Abstract

In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas–Rachford splitting method. Our algorithm performs both function and variable splittings. It sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach leverages the proximity operator of the logistic loss, which is expressed with the generalized Lambert W function. Experiments carried out on standard datasets demonstrate the efficiency of our approach w. r. t. stochastic gradient-like methods.

Suggested Citation

  • Luis M. Briceño-Arias & Giovanni Chierchia & Emilie Chouzenoux & Jean-Christophe Pesquet, 2019. "A random block-coordinate Douglas–Rachford splitting method with low computational complexity for binary logistic regression," Computational Optimization and Applications, Springer, vol. 72(3), pages 707-726, April.
    • Handle: RePEc:spr:coopap:v:72:y:2019:i:3:d:10.1007_s10589-019-00060-6
    DOI: 10.1007/s10589-019-00060-6
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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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    5. Patrick L. Combettes & Jean-Christophe Pesquet, 2011. "Proximal Splitting Methods in Signal Processing," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 185-212, Springer.
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