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Mixed Integer Second-Order Cone Programming Formulations for Variable Selection

Ryuhei Miyashiro (r-miya***at***cc.tuat.ac.jp)
Yuichi Takano (takano.y.ad***at***m.titech.ac.jp)

Abstract: This paper concerns the method of selecting the best subset of explanatory variables in a multiple linear regression model. To evaluate a subset regression model, some goodness-of-fit measures, e.g., adjusted R^2, AIC and BIC, are generally employed. Although variable selection is usually handled via a stepwise regression method, the method does not always provide the best subset of explanatory variables according to adjusted R^2, AIC and BIC. In this paper, we propose mixed integer second-order cone programming formulations for selecting the best subset of variables. Computational experiments show that, in terms of the goodness-of-fit measures, the proposed formulations yield solutions having a clear advantage over common stepwise regression methods.

Keywords: Integer programming, Variable selection, Multiple linear regression, Information criterion, Second-order cone programming, Statistics

Category 1: Integer Programming ((Mixed) Integer Nonlinear Programming )

Category 2: Linear, Cone and Semidefinite Programming (Second-Order Cone Programming )

Category 3: Applications -- Science and Engineering (Statistics )

Citation: Published as: R. Miyashiro and Y. Takano, Mixed integer second-order cone programming formulations for variable selection in linear regression. European Journal of Operational Research, 247(3), pp. 721-731, 2015.

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Entry Submitted: 06/25/2013
Entry Accepted: 06/25/2013
Entry Last Modified: 09/30/2016

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