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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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    3. Liu, Yufeng & Helen Zhang, Hao & Park, Cheolwoo & Ahn, Jeongyoun, 2007. "Support vector machines with adaptive Lq penalty," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6380-6394, August.
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    6. Jonathan Eckstein, 2017. "A Simplified Form of Block-Iterative Operator Splitting and an Asynchronous Algorithm Resembling the Multi-Block Alternating Direction Method of Multipliers," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 155-182, April.
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