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Selective linearization for multi-block statistical learning

Author

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  • Du, Yu
  • Lin, Xiaodong
  • Pham, Minh
  • Ruszczyński, Andrzej

Abstract

We consider the problem of minimizing a sum of several convex non-smooth functions and discuss the selective linearization method (SLIN), which iteratively linearizes all but one of the functions and employs simple proximal steps. The algorithm is a form of multiple operator splitting in which the order of processing partial functions is not fixed, but rather determined in the course of calculations. SLIN is globally convergent for an arbitrary number of component functions without artificial duplication of variables. We report results from extensive numerical experiments in two statistical learning settings such as large-scale overlapping group Lasso and doubly regularized support vector machine. In each setting, we introduce novel and efficient solutions for solving sub-problems. The numerical results demonstrate the efficacy and accuracy of SLIN.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:293:y:2021:i:1:p:219-228
    DOI: 10.1016/j.ejor.2020.12.010
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    References listed on IDEAS

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    1. Yu Du & Andrzej Ruszczyński, 2017. "Rate of Convergence of the Bundle Method," Journal of Optimization Theory and Applications, Springer, vol. 173(3), pages 908-922, June.
    2. 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.
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    4. Olafsson, Sigurdur & Li, Xiaonan & Wu, Shuning, 2008. "Operations research and data mining," European Journal of Operational Research, Elsevier, vol. 187(3), pages 1429-1448, June.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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