具有环面消失理想的对称彩色高斯图形模型

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2021-11-29 DOI:10.1137/21M1466943

Jane Ivy Coons, Aida Maraj, Pratik Misra, Miruna-Stefana Sorea

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引用次数: 1

摘要

有色高斯图形模型是一种线性浓度模型，其中浓度之间的等式通过底层图形的着色来指定。如果这种着色是由图的自同构群的一个子群的边和顶点轨道给出的，则该模型称为RCOP。我们证明了块图上的RCOP高斯图形模型在协方差矩阵空间上是环面的，并描述了它们的马尔可夫基。为此，我们更多地了解了这些模型的组合结构以及它们与Jordan代数的联系。

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Symmetrically Colored Gaussian Graphical Models with Toric Vanishing Ideals

A colored Gaussian graphical model is a linear concentration model in which equalities among the concentrations are specified by a coloring of an underlying graph. The model is called RCOP if this coloring is given by the edge and vertex orbits of a subgroup of the automorphism group of the graph. We show that RCOP Gaussian graphical models on block graphs are toric in the space of covariance matrices and we describe Markov bases for them. To this end, we learn more about the combinatorial structure of these models and their connection with Jordan algebras.

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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量