Date: Friday, January 28, 2022
Location: 4088 East Hall (3:00 PM to 4:00 PM)
Title: Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals
Abstract: A Colored Gaussian graphical model is a collection of multivariate Gaussian distributions in which a colored graph encodes conditional independence relations among the random variables. Its set of concentration matrices is a linear space of symmetric matrices intersected with the cone of positive definite matrices. Its inverse space, the space of covariance matrices, on the contrary, most often does not have a friendly structure. Given that entries of the covariance matrices are statistically significant, knowing equations defining them is a question of interest. 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 graph has a block structure, the set of covariance 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 which can be read from paths in the graph. The talk is based on the arxiv preprint arXiv:2111.14817.
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Speaker: Aida Maraj
Institution: University of Michigan
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