Lattices of Graphical Gaussian Models with Symmetries

Symmetry

关键词: conditional independence;    covariance selection;    invariance;    model selection;    patterned covariance matrices;    permutation symmetry;   

DOI  :  10.3390/sym3030653

来源: mdpi

【 摘 要 】

In order to make graphical Gaussian models a viable modelling tool when the number of variables outgrows the number of observations, [1] introduced model classes which place equality restrictions on concentrations or partial correlations. The models can be represented by vertex and edge coloured graphs. The need for model selection methods makes it imperative to understand the structure of model classes. We identify four model classes that form complete lattices of models with respect to model inclusion, which qualifies them for an Edwards–Havránek model selection procedure [2]. Two classes turn out most suitable for a corresponding model search. We obtain an explicit search algorithm for one of them and provide a model search example for the other.

【 授权许可】

CC BY   
This is an open access article distributed under the Creative Commons Attribution License (CC BY) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.