Computing Maximum Likelihood Estimates for Gaussian Graphical Models with Macaulay2
Carlos Am\'endola, Luis David Garc\'ia Puente, Roser Homs, Olga, Kuznetsova, Harshit J. Motwani
TL;DR
This paper presents a Macaulay2 package for computing maximum likelihood estimates of Gaussian graphical models, enabling algebraic exploration of model properties like MLE degree and score equations.
Contribution
It introduces the GraphicalModelsMLE package, providing tools for MLE computation and algebraic analysis of Gaussian graphical models in Macaulay2.
Findings
Successfully computes MLEs for loopless mixed graphs
Allows exploration of algebraic properties like MLE degree
Facilitates algebraic analysis of Gaussian graphical models
Abstract
We introduce the package "GraphicalModelsMLE" for computing the maximum likelihood estimates (MLEs) of a Gaussian graphical model in the computer algebra system Macaulay2. This package allows the computation of MLEs for the class of loopless mixed graphs. Additional functionality allows the user to explore the underlying algebraic structure of the model, such as its maximum likelihood degree and the ideal of score equations.
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Taxonomy
TopicsBayesian Modeling and Causal Inference · Computational Drug Discovery Methods · Topological and Geometric Data Analysis