Graphical Gaussian models with edge and vertex symmetries
AbstractWe 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 parameters that are associated with edges or vertices of the same colour are restricted to being identical. We study the properties of such models and derive the necessary algorithms for calculating maximum likelihood estimates. We identify conditions for restrictions on the concentration and correlation matrices being equivalent. This is for example the case when symmetries are generated by permutation of variable labels. For such models a particularly simple maximization of the likelihood function is available. Copyright (c) 2008 Royal Statistical Society.
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Bibliographic InfoArticle provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).
Volume (Year): 70 (2008)
Issue (Month): 5 ()
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- Bernd Sturmfels & Caroline Uhler, 2010. "Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(4), pages 603-638, August.
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