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Jane Coons: Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals

Time: Tue 2022-02-08 10.15

Location: Zoom

Video link: Meeting ID: 659 3743 5667

Lecturer: Jane Coons (St John's College at the University of Oxford)

Abstract

Gaussian graphical models are multivariate Gaussian statistical models in which a graph encodes conditional independence relations among the random variables. Adding colors to this graph allows us to describe situations where some entries in the concentration matrices in the model are assumed to be equal. In this talk, we focus on RCOP models, in which this coloring is obtained from the orbits of a subgroup of the automorphism group of the underlying graph. We show that when the underlying block graph is a one-clique-sum of complete graphs, the Zariski closure of the set of concentration matrices of an RCOP model on this graph is a toric variety. We also give a Markov basis for the vanishing ideal of this variety in these cases.