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Subset Selection by Mallows' Cp: A Mixed Integer Programming Approach

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

Abstract: This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows' C_p as a goodness-of-fit measure, we formulate the subset selection problem as a mixed integer quadratic programming problem. Computational results demonstrate that our method provides the best subset of variables in a few seconds when the number of candidate explanatory variables is less than 30. Furthermore, when handling datasets consisting of a large number of samples, it finds better-quality solutions faster than stepwise regression methods do.

Keywords: Subset selection, Mixed integer programming, Mallows' C_p, Linear regression model

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

Category 2: Nonlinear Optimization (Quadratic Programming )

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

Citation: Published in Expert Systems with Applications, 42 (2015), 325-331.

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Entry Submitted: 01/18/2014
Entry Accepted: 01/18/2014
Entry Last Modified: 09/04/2014

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