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An efficient optimization approach for best subset selection in linear regression, with application to model selection and fitting in autoregressive time-series

Author

Listed:
  • Leonardo Di Gangi

    (Università degli Studi di Firenze)

  • M. Lapucci

    (Università degli Studi di Firenze)

  • F. Schoen

    (Università degli Studi di Firenze)

  • A. Sortino

    (Università degli Studi di Firenze)

Abstract

In this paper we consider two relevant optimization problems: the problem of selecting the best sparse linear regression model and the problem of optimally identifying the parameters of auto-regressive models based on time series data. Usually these problems, which although different are indeed related, are solved through a sequence of separate steps, alternating between choosing a subset of features and then finding a best fit regression. In this paper we propose to model both problems as mixed integer non linear optimization ones and propose numerical procedures based on state of the art optimization tools in order to solve both of them. The proposed approach has the advantage of considering both model selection as well as parameter estimation as a single optimization problem. Numerical experiments performed on widely available datasets as well as on synthetic ones confirm the high quality of our approach, both in terms of the quality of the resulting models and in terms of CPU time.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:74:y:2019:i:3:d:10.1007_s10589-019-00134-5
    DOI: 10.1007/s10589-019-00134-5
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    References listed on IDEAS

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    1. Miyashiro, Ryuhei & Takano, Yuichi, 2015. "Mixed integer second-order cone programming formulations for variable selection in linear regression," European Journal of Operational Research, Elsevier, vol. 247(3), pages 721-731.
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    8. 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.
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    Cited by:

    1. 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.
    2. 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.

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