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Recent advances in mathematical programming have made Mixed IntegerOptimization a competitive alternative to popular regularization methods forselecting features in regression problems. The approach exhibits unquestionablefoundational appeal and versatility, but also poses important challenges. Herewe propose MIP-BOOST, a revision of standard Mixed Integer Programming featureselection that reduces the computational burden of tuning the critical sparsitybound parameter and improves performance in the presence of featurecollinearity and of signals that vary in nature and strength. The final outcomeis a more efficient and effective $L_0$ Feature Selection method forapplications of realistic size and complexity, grounded on rigorouscross-validation tuning and exact optimization of the associated Mixed IntegerProgram. Computational viability and improved performance in realisticscenarios is achieved through three independent but synergistic proposals.

MIP-BOOST: Efficient and Effective $L_0$ Feature Selection for Linear Regression