Mixed integer second-order cone programming formulations for variable selection in linear regression

• AIC/BIC minimization, and adjusted R2 maximization problems are considered.
• These problems are formulated as mixed integer second-order cone programming problems.
• Experiments shows results of better quality than obtained by stepwise regression.

This study concerns a method of selecting the best subset of explanatory variables in a multiple linear regression model. Goodness-of-fit measures, for example, adjusted R2, AIC, and BIC, are generally used to evaluate a subset regression model. Although variable selection with regard to these measures is usually performed with a stepwise regression method, it does not always provide the best subset of explanatory variables. In this paper, we propose mixed integer second-order cone programming formulations for selecting the best subset of variables with respect to adjusted R2, AIC, and BIC. Computational experiments show that, in terms of these measures, the proposed formulations yield better solutions than those provided by common stepwise regression methods.