On the maximum likelihood degree for Gaussian graphical models

2024/10/09 by Carlos Améndola, Rodica Dinu, Améndola, Carlos +5 · 2 citations
Computer Science · #Algebraic Geometry (math.AG) #Bayesian Modeling and Causal Inference #FOS: Mathematics #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2410.07007

openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we revisit the likelihood geometry of Gaussian graphical models. We give a detailed proof that the ML-degree behaves monotonically on induced subgraphs. Furthermore, we complete a missing argument that the ML-degree of the n-th cycle is larger than one for any n≥ 4, therefore completing the characterization that the only Gaussian graphical models with rational maximum likelihood estimator are the ones corresponding to chordal (decomposable) graphs. Finally, we prove that the formula for the ML-degree of a cycle conjectured by Drton, Sturmfels and Sullivant provides a correct lower bound.

Cited by

• Characteristic numbers of algebras
• The Maximum Likelihood Degree of Toric Models is Monotonic

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