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arXiv · 2411.03139

Lattice supported distributions and graphical models

Thomas Kahle·Seth Sullivant
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Abstract

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.

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Thomas Kahle, Seth Sullivant. 2024-11-05. Lattice supported distributions and graphical models. https://arxiv.org/abs/2411.03139

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