• Corpus ID: 227254569

Coloured Graphical Models and their Symmetries.

@article{Davies2020ColouredGM,
  title={Coloured Graphical Models and their Symmetries.},
  author={Isobel Davies and Orlando Marigliano},
  journal={arXiv: Algebraic Geometry},
  year={2020}
}
Coloured graphical models are Gaussian statistical models determined by an undirected coloured graph. These models can be described by linear spaces of symmetric matrices. We outline a relationship between the symmetries of the graph and the linear forms that vanish on the reciprocal variety of the model. In the special case of the uniform coloured n-cycle, this gives a complete description of all such linear forms. 

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References

SHOWING 1-6 OF 6 REFERENCES
Graphical Gaussian models with edge and vertex symmetries
Summary.  We introduce new types of graphical Gaussian models by placing symmetry restrictions on the concentration or correlation matrix. The models can be represented by coloured graphs, where
Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry
We study multivariate normal models that are described by linear constraints on the inverse of the covariance matrix. Maximum likelihood estimation for such models leads to the problem of maximizing
Algebraic statistics
TLDR
This tutorial will consist of a detailed study of two examples where the algebra/statistics connection has proven especially useful: in the study of phylogenetic models and in the analysis of contingency tables.
Pencils of Quadrics: Old and New
Two-dimensional linear spaces of symmetric matrices are classified by Segre symbols. After reviewing known facts from linear algebra and projective geometry, we address new questions motivated by
Algebraic statistics, American Mathematical Society, 2018
  • ISOBEL DAVIES Max Planck Institute for Mathematics in the Sciences Inselstraße
  • 2018
Algebraic Graph Theory
TLDR
The Laplacian of a Graph and Cuts and Flows are compared to the Rank Polynomial.