Holistic Generalized Linear Models

Abstract: Holistic linear regression extends the classical best subset selection problem by adding additional constraints designed to improve the model quality. These constraints include sparsity-inducing constraints, sign-coherence constraints and linear constraints. The $\textsf{R}$ package $\texttt{holiglm}$ provides functionality to model and fit holistic generalized linear models. By making use of state-of-the-art conic mixed-integer solvers, the package can reliably solve GLMs for Gaussian, binomial and Poisson responses with a multitude of holistic constraints. The high-level interface simplifies the constraint specification and can be used as a drop-in replacement for the $\texttt{stats::glm()}$ function.