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Graphical Gaussian models with edge and vertex symmetries
Author(s) -
Højsgaard Søren,
Lauritzen Steffen L.
Publication year - 2008
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2008.00666.x
Subject(s) - homogeneous space , graphical model , gaussian , simple (philosophy) , mathematics , vertex (graph theory) , permutation (music) , symmetry (geometry) , combinatorics , maximization , likelihood function , function (biology) , enhanced data rates for gsm evolution , gaussian network model , expectation–maximization algorithm , matrix (chemical analysis) , maximum likelihood , algorithm , computer science , graph , mathematical optimization , geometry , artificial intelligence , statistics , physics , philosophy , materials science , acoustics , composite material , biology , epistemology , quantum mechanics , evolutionary biology
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 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.