On the maximum likelihood degree for Gaussian graphical models
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866916429471678464 |
|---|---|
| author | Améndola, Carlos Dinu, Rodica Andreea Michałek, Mateusz Vodička, Martin |
| author_facet | Améndola, Carlos Dinu, Rodica Andreea Michałek, Mateusz Vodička, Martin |
| contents | 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 $n\geq 4$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_07007 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the maximum likelihood degree for Gaussian graphical models Améndola, Carlos Dinu, Rodica Andreea Michałek, Mateusz Vodička, Martin Statistics Theory Algebraic Geometry 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 $n\geq 4$, 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. |
| title | On the maximum likelihood degree for Gaussian graphical models |
| topic | Statistics Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.07007 |