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An effective procedure for feature subset selection in logistic regression based on information criteria

Author

Listed:
  • Enrico Civitelli

    (Università degli Studi di Firenze)

  • Matteo Lapucci

    (Università degli Studi di Firenze)

  • Fabio Schoen

    (Università degli Studi di Firenze)

  • Alessio Sortino

    (Università degli Studi di Firenze)

Abstract

In this paper, the problem of best subset selection in logistic regression is addressed. In particular, we take into account formulations of the problem resulting from the adoption of information criteria, such as AIC or BIC, as goodness-of-fit measures. There exist various methods to tackle this problem. Heuristic methods are computationally cheap, but are usually only able to find low quality solutions. Methods based on local optimization suffer from similar limitations as heuristic ones. On the other hand, methods based on mixed integer reformulations of the problem are much more effective, at the cost of higher computational requirements, that become unsustainable when the problem size grows. We thus propose a new approach, which combines mixed-integer programming and decomposition techniques in order to overcome the aforementioned scalability issues. We provide a theoretical characterization of the proposed algorithm properties. The results of a vast numerical experiment, performed on widely available datasets, show that the proposed method achieves the goal of outperforming state-of-the-art techniques.

Suggested Citation

  • Enrico Civitelli & Matteo Lapucci & Fabio Schoen & Alessio Sortino, 2021. "An effective procedure for feature subset selection in logistic regression based on information criteria," Computational Optimization and Applications, Springer, vol. 80(1), pages 1-32, September.
    • Handle: RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00288-1
    DOI: 10.1007/s10589-021-00288-1
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    References listed on IDEAS

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    1. Leonardo Di Gangi & M. Lapucci & F. Schoen & A. Sortino, 2019. "An efficient optimization approach for best subset selection in linear regression, with application to model selection and fitting in autoregressive time-series," Computational Optimization and Applications, Springer, vol. 74(3), pages 919-948, December.
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    3. Toshiki Sato & Yuichi Takano & Ryuhei Miyashiro & Akiko Yoshise, 2016. "Feature subset selection for logistic regression via mixed integer optimization," Computational Optimization and Applications, Springer, vol. 64(3), pages 865-880, July.
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    6. Zemin Zheng & Yingying Fan & Jinchi Lv, 2014. "High dimensional thresholded regression and shrinkage effect," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 627-649, June.
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