Lattice supported distributions and graphical models

Fuente: arXiv
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Autori principali: Kahle, Thomas, Sullivant, Seth
Natura: Preprint
Pubblicazione: 2024
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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