Coloured Graphical Gaussian Models

 

Undirected graphical Gaussian models restricts elements of the concentration (inverse covariance) matrix K to being zero whenever the associated variables are conditionally independent given the remaining.

We introduce coloured graphical models by partitioning the vertices of the graph in vertex colour classes and the edges in edge colour classes. Models of one type restrict elements in K to being identical if the corresponding vertices/edges are in the same colour class. Another type of models restrict partial correlations to being identical. A subset of these models are determined by invariance under special permutations.

The properties of the models and associated estimation algorithms are discussed and illustrated.

This represents joint work with Soren Hojsgaard, Danish Institute of Agricultural Research.