Automated subset selection via information criteria optimization in generalized linear models

Abstract In this paper, we show how mixed-integer conic programming can be used to directly optimize information criteria such as AIC and BIC in order to automate the model selection process for a collection of GLMs. Moreover, we propose to enhance the optimization problem with a novel linear constraint that limits pairwise correlation between the selected features and is well suited to tackle pairwise multicollinearity. Through a simulation study, we show that the proposed approach achieves high accuracy in selecting the active coefficients and outperforms naive enumeration methods aimed at subset selection.