Binomiality of colored Gaussian models

2025/07/08 by Biaggi, Benjamin, Draisma, Jan, Mišinová, Magdaléna
#62R01 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Statistics Theory (math.ST)

paper · doi:10.48550/arxiv.2507.06437

Abstract

Following earlier work by Coons-Maraj-Misra-Sorea and Misra-Sullivant, we study colored, undirected Gaussian graphical models, and present a necessary and sufficient condition for such a model to have binomial vanishing ideal. These conditions involve Jordan schemes, a variant of association schemes, well-known structures in algebraic combinatorics. Using association schemes without transitive group action, we refute the conjecture by Coons-Maraj-Misra-Sorea that binomiality implies that the color classes must be orbits under the automorphism group of the colored graph.

Citations

• Efficiently deciding if an ideal is toric after a linear coordinate change
• Symmetry Lie Algebras of Varieties with Applications to Algebraic Statistics
• The three-state toric homogeneous Markov chain model has Markov degree two
• Determinants of weighted path matrices
• Multivariate Gaussians, Semidefinite Matrix Completion, and Convex Algebraic Geometry
• Toric ideals of phylogenetic invariants
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Related

• Linear relations of colored Gaussian cycles
• Gaussian graphical models with toric vanishing ideals
• Coloured Graphical Models and their Symmetries
• Toric Multivariate Gaussian Models from Symmetries in a Tree
• Transitive and Gallai colorings