On the maximum likelihood degree of Gaussian graphical models
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 cycle is larger than 1 for any , 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.
Authors
- Mateusz Michałek (ORCID: https://orcid.org/0000-0002-6081-786X)
- Martin Vodička (ORCID: https://orcid.org/0009-0007-3976-4007)
- Rodica Dinu (ORCID: https://orcid.org/0000-0001-7424-9050)
- Carlos Améndola (ORCID: https://orcid.org/0000-0003-1945-8874)
Institutions
- University of Konstanz (DE)
- University of Pavol Jozef Šafárik (SK)
- IMAR - Institutul de Matematică „Simion Stoilow” al Academiei Române (RO)
- Technische Universität Berlin (DE)
- Romanian Academy (RO)
Publication Details
- Journal
- Bulletin of the London Mathematical Society
- Published
- 2026-09-21
- DOI
- https://doi.org/10.1112/blms.70507
- Primary Topic
- Bayesian Modeling and Causal Inference
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- Alexander von Humboldt-Stiftung
- Deutsche Forschungsgemeinschaft
- Vedecká Grantová Agentúra MŠVVaŠ SR a SAV