Lattice supported distributions and 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_ | 1866916468764966912 |
|---|---|
| author | Kahle, Thomas Sullivant, Seth |
| author_facet | Kahle, Thomas Sullivant, Seth |
| contents | For the distributions of finitely many binary random variables, we study the interaction of restrictions of the supports with conditional independence constraints. We prove a generalization of the Hammersley-Clifford theorem for distributions whose support is a natural distributive lattice: that is, any distribution which has natural lattice support and satisfies the pairwise Markov statements of a graph must factor according to the graph. We also show a connection to the Hibi ideals of lattices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03139 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Lattice supported distributions and graphical models Kahle, Thomas Sullivant, Seth Statistics Theory Commutative Algebra Algebraic Geometry Combinatorics 62R01, 13C70, 05E40, 06D99 For the distributions of finitely many binary random variables, we study the interaction of restrictions of the supports with conditional independence constraints. We prove a generalization of the Hammersley-Clifford theorem for distributions whose support is a natural distributive lattice: that is, any distribution which has natural lattice support and satisfies the pairwise Markov statements of a graph must factor according to the graph. We also show a connection to the Hibi ideals of lattices. |
| title | Lattice supported distributions and graphical models |
| topic | Statistics Theory Commutative Algebra Algebraic Geometry Combinatorics 62R01, 13C70, 05E40, 06D99 |
| url | https://arxiv.org/abs/2411.03139 |