Holistic Generalized Linear Models

TL;DR

This paper introduces holistic generalized linear models that incorporate additional constraints to improve model quality, implemented in an R package that reliably solves various GLMs with holistic constraints.

Contribution

It presents a new class of constrained GLMs and an R package that simplifies their modeling and fitting using advanced conic mixed-integer solvers.

Findings

Successfully models Gaussian, binomial, and Poisson responses with holistic constraints.

Provides a user-friendly high-level interface for constrained GLMs.

Enhances model quality through sparsity, sign-coherence, and linear constraints.

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.