Subset selection by Mallows’ CpCp: A mixed integer programming approach

• A subset selection problem with respect to Mallows’ CpCp is considered.
• The problem is formulated as a mixed integer quadratic programming problem.
• For small instances, the MIQP approach provides optimal solutions in a few seconds.
• For large instances, the MIQP approach is faster than stepwise regression methods.

This paper concerns a method of selecting the best subset of explanatory variables for a linear regression model. Employing Mallows’ CpCp 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.