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Computing maximum likelihood estimates for Gaussian graphical models with Macaulay2

Carlos Améndola, Luis David García Puente, Roser Homs, Olga Kuznetsova and Harshit J. Motwani

Vol. 12 (2022), 1–10

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.

algebraic statistics, Gaussian graphical models, loopless mixed graphs, MLE
Mathematical Subject Classification
Primary: 62F10, 62H22, 62R01
Supplementary material

Macaulay2 package for computing the maximum likelihood estimates of Gaussian graphical models

Received: 22 December 2020
Revised: 30 November 2021
Accepted: 14 March 2022
Published: 20 November 2022
Carlos Améndola
Max Planck Institute for Mathematics in the Sciences
Luis David García Puente
Department of Mathematics and Computer Science
Colorado College
Colorado Springs, CO
United States
Roser Homs
Department of Mathematics
Technical University of Munich
Olga Kuznetsova
Department of Mathematics and Systems Analysis
Aalto University
Harshit J. Motwani
Department of Mathematics: Algebra and Geometry
Ghent University