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New bounds for subset selection from conic relaxations

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  • Ben-Ameur, Walid
  • Neto, José

Abstract

New bounds are proposed for the subset selection problem which consists in minimizing the residual sum of squares subject to a cardinality constraint on the maximum number of non-zero variables. They rely on new convex relaxations providing both upper and lower bounds that are compared with others present in the literature. The performance of these methods is illustrated through computational experiments.

Suggested Citation

  • Ben-Ameur, Walid & Neto, José, 2022. "New bounds for subset selection from conic relaxations," European Journal of Operational Research, Elsevier, vol. 298(2), pages 425-438.
    • Handle: RePEc:eee:ejores:v:298:y:2022:i:2:p:425-438
    DOI: 10.1016/j.ejor.2021.07.011
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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.
    2. 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.
    3. Mazumder, Rahul & Friedman, Jerome H. & Hastie, Trevor, 2011. "SparseNet: Coordinate Descent With Nonconvex Penalties," Journal of the American Statistical Association, American Statistical Association, vol. 106(495), pages 1125-1138.
    4. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
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