Holistic Generalized Linear Models
This work provides a tool for statisticians and data analysts to fit more robust GLMs with constraints, but it is incremental as it builds on existing best subset selection methods.
The authors tackled the problem of improving model quality in generalized linear models by extending best subset selection with additional constraints like sparsity and sign-coherence, resulting in a new R package, holiglm, that reliably solves these models using conic mixed-integer solvers for Gaussian, binomial, and Poisson responses.
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.