Marginal Independence and Partial Set Partitions
Statistics Theory
2025-04-02 v2 Algebraic Geometry
Combinatorics
Statistics Theory
Abstract
We establish a bijection between marginal independence models on random variables and split closed order ideals in the poset of partial set partitions. We also establish that every discrete marginal independence model is toric in cdf coordinates. This generalizes results of Boege, Petrovic, and Sturmfels and Drton and Richardson, and provides a unified framework for discussing marginal independence models. Additionally, we provide an axiomatic characterization of marginal independence and we show that our set of axioms are sound and complete in the set of probability distributions. This follows the work of Geiger, Paz and Pearl who provided an analogous characterization of independence for statements involving 2 sets of random variables.
Cite
@article{arxiv.2402.16292,
title = {Marginal Independence and Partial Set Partitions},
author = {Francisco Ponce-Carrión and Seth Sullivant},
journal= {arXiv preprint arXiv:2402.16292},
year = {2025}
}