Graphical models in Macaulay2

TL;DR

This paper introduces a Macaulay2 package that provides algorithms for algebraic analysis of various graphical models, enabling computation of ideals, independence statements, and parameter identifiability.

Contribution

It presents new computational tools within Macaulay2 for algebraic analysis of graphical models, including ideal computation and parameter identifiability checks.

Findings

Algorithms for vanishing ideal computation

Procedures for generating conditional independence ideals

Methods for checking parameter identifiability in Gaussian models

Abstract

The Macaulay2 package GraphicalModels contains algorithms for the algebraic study of graphical models associated to undirected, directed and mixed graphs, and associated collections of conditional independence statements. Among the algorithms implemented are procedures for computing the vanishing ideal of graphical models, for generating conditional independence ideals of families of independence statements associated to graphs, and for checking for identifiable parameters in Gaussian mixed graph models. These procedures can be used to study fundamental problems about graphical models.