IDEAS home Printed from https://ideas.repec.org/a/spr/coopap/v80y2021i1d10.1007_s10589-021-00288-1.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10589-021-00288-1
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10589-021-00288-1?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. P. Tseng, 2001. "Convergence of a Block Coordinate Descent Method for Nondifferentiable Minimization," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 475-494, June.
    2. 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.
    3. 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.
    4. F. Rinaldi & F. Schoen & M. Sciandrone, 2010. "Concave programming for minimizing the zero-norm over polyhedral sets," Computational Optimization and Applications, Springer, vol. 46(3), pages 467-486, July.
    5. 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.
    6. Xiaotong Shen & Wei Pan & Yunzhang Zhu & Hui Zhou, 2013. "On constrained and regularized high-dimensional regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(5), pages 807-832, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.
    2. Manlio Gaudioso & Giovanni Giallombardo & Giovanna Miglionico, 2023. "Sparse optimization via vector k-norm and DC programming with an application to feature selection for support vector machines," Computational Optimization and Applications, Springer, vol. 86(2), pages 745-766, November.
    3. Matteo Lapucci & Tommaso Levato & Marco Sciandrone, 2021. "Convergent Inexact Penalty Decomposition Methods for Cardinality-Constrained Problems," Journal of Optimization Theory and Applications, Springer, vol. 188(2), pages 473-496, February.
    4. Shuang Zhang & Xingdong Feng, 2022. "Distributed identification of heterogeneous treatment effects," Computational Statistics, Springer, vol. 37(1), pages 57-89, March.
    5. Jung, Yoon Mo & Whang, Joyce Jiyoung & Yun, Sangwoon, 2020. "Sparse probabilistic K-means," Applied Mathematics and Computation, Elsevier, vol. 382(C).
    6. Sauvenier, Mathieu & Van Bellegem, Sébastien, 2023. "Direction Identification and Minimax Estimation by Generalized Eigenvalue Problem in High Dimensional Sparse Regression," LIDAM Discussion Papers CORE 2023005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Seunghwan Lee & Sang Cheol Kim & Donghyeon Yu, 2023. "An efficient GPU-parallel coordinate descent algorithm for sparse precision matrix estimation via scaled lasso," Computational Statistics, Springer, vol. 38(1), pages 217-242, March.
    8. Le Thi Khanh Hien & Duy Nhat Phan & Nicolas Gillis, 2022. "Inertial alternating direction method of multipliers for non-convex non-smooth optimization," Computational Optimization and Applications, Springer, vol. 83(1), pages 247-285, September.
    9. Liu, De-Chih & Chang, Yu-Chien, 2022. "Systematic variations in exchange rate returns," International Review of Economics & Finance, Elsevier, vol. 82(C), pages 569-583.
    10. Zemin Zheng & Jie Zhang & Yang Li, 2022. "L 0 -Regularized Learning for High-Dimensional Additive Hazards Regression," INFORMS Journal on Computing, INFORMS, vol. 34(5), pages 2762-2775, September.
    11. Victor Chernozhukov & Whitney K. Newey & Victor Quintas-Martinez & Vasilis Syrgkanis, 2021. "Automatic Debiased Machine Learning via Riesz Regression," Papers 2104.14737, arXiv.org, revised Mar 2024.
    12. Yuezhang Che & Shuyan Chen & Xin Liu, 2022. "Sparse Index Tracking Portfolio with Sector Neutrality," Mathematics, MDPI, vol. 10(15), pages 1-22, July.
    13. Paul Tseng, 2004. "An Analysis of the EM Algorithm and Entropy-Like Proximal Point Methods," Mathematics of Operations Research, INFORMS, vol. 29(1), pages 27-44, February.
    14. Omer, E. & Guetta, R. & Ioslovich, I. & Gutman, P.O. & Borshchevsky, M., 2008. "“Energy Tower” combined with pumped storage and desalination: Optimal design and analysis," Renewable Energy, Elsevier, vol. 33(4), pages 597-607.
    15. Luke Mosley & Idris A. Eckley & Alex Gibberd, 2022. "Sparse temporal disaggregation," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(4), pages 2203-2233, October.
    16. David Degras, 2021. "Sparse group fused lasso for model segmentation: a hybrid approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(3), pages 625-671, September.
    17. Masoud Ahookhosh & Le Thi Khanh Hien & Nicolas Gillis & Panagiotis Patrinos, 2021. "A Block Inertial Bregman Proximal Algorithm for Nonsmooth Nonconvex Problems with Application to Symmetric Nonnegative Matrix Tri-Factorization," Journal of Optimization Theory and Applications, Springer, vol. 190(1), pages 234-258, July.
    18. Astorino, Annabella & Avolio, Matteo & Fuduli, Antonio, 2022. "A maximum-margin multisphere approach for binary Multiple Instance Learning," European Journal of Operational Research, Elsevier, vol. 299(2), pages 642-652.
    19. Wenxing Zhu & Huating Huang & Lanfan Jiang & Jianli Chen, 0. "Weighted thresholding homotopy method for sparsity constrained optimization," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-29.
    20. Canhong Wen & Zhenduo Li & Ruipeng Dong & Yijin Ni & Wenliang Pan, 2023. "Simultaneous Dimension Reduction and Variable Selection for Multinomial Logistic Regression," INFORMS Journal on Computing, INFORMS, vol. 35(5), pages 1044-1060, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:coopap:v:80:y:2021:i:1:d:10.1007_s10589-021-00288-1. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.