# Marginal Independence Models

arXiv: https://arxiv.org/abs/2112.10287 · HTML: https://mlsanity.com/paper/2112.10287/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Dec 2021.

## Built on by (most cited first, 1 of 1)

- [Combinatorial and algebraic perspectives on the marginal independence structure of Bayesian networks](https://mlsanity.com/paper/2210.00822/) (2022)

## Abstract (arXiv)

We impose rank one constraints on marginalizations of a tensor, given by a simplicial complex. Following work of Kirkup and Sullivant, such marginal independence models can be made toric by a linear change of coordinates. We study their toric ideals, with emphasis on random graph models and independent set polytopes of matroids. We develop the numerical algebra of parameter estimation, using both Euclidean distance and maximum likelihood, and we present a comprehensive database of small models.