# Marginal Independence Models

@article{Boege2021MarginalIM, title={Marginal Independence Models}, author={Tobias Boege and Sonja Petrovi'c and Bernd Sturmfels}, journal={ArXiv}, year={2021}, volume={abs/2112.10287} }

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.

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SHOWING 1-10 OF 28 REFERENCES

Combinatorial Degree Bound for Toric ideals of hypergraphs

- MathematicsInt. J. Algebra Comput.
- 2013

This work recovers a well-known complexity result for Markov bases of arbitrary 3-way tables, and shows that the defining ideal of the tangential variety is generated by quadratics and cubics in cumulant coordinates.

Algebraic properties of toric rings of graphs

- MathematicsCommunications in Algebra
- 2019

Abstract Let be a simple graph. We investigate the Cohen–Macaulayness and algebraic invariants, such as the Castelnuovo-Mumford regularity and the projective dimension, of the toric ring k[G] via…

Toric algebra of hypergraphs

- Mathematics
- 2012

The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of…

Gröbner Bases and Polyhedral Geometry of Reducible and Cyclic Models

- Mathematics, Computer ScienceJ. Comb. Theory, Ser. A
- 2002

The polyhedral structure and combinatorics of polytopes that arise from hierarchical models in statistics are studied, and it is shown how to construct Grobner bases of toric ideals associated to a subset of such models.

The Toric Ideal of a Matroid of Rank 3 is Generated by Quadrics

- MathematicsElectron. J. Comb.
- 2010

A combinatorial proof of White's conjecture that the toric ideal associated with the basis of a matroid is generated by quadrics corresponding to symmetric exchanges is presented by using a lemma proposed by Blasiak.

The Euclidean Distance Degree of an Algebraic Variety

- MathematicsFound. Comput. Math.
- 2016

A theory of such nearest point maps of a real algebraic variety with respect to Euclidean distance from the perspective of computational algebraic geometry is developed.

The toric ideal of a graphic matroid is generated by quadrics

- MathematicsComb.
- 2008

A combinatorial proof of Neil White’s conjecture that the toric ideal associated to a matroid is generated by quadrics corresponding to single element symmetric exchanges for graphic matroids is given.