A Mixed-Integer Fractional Optimization Approach to Best Subset Selection

Abstract

We consider the best subset selection problem in linear regression—that is, finding a parsimonious subset of the regression variables that provides the best fit to the data according to some predefined criterion. We are primarily concerned with alternatives to cross-validation methods that do not require data partitioning and involve a range of information criteria extensively studied in the statistical literature. We show that the problem of interest can be modeled using fractional mixed-integer optimization, which can be tackled by Show more