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Inferring a graphical model or network from observational data from a largenumber of variables is a well studied problem in machine learning andcomputational statistics. In this paper we consider a version of this problemthat is relevant to the analysis of multiple phenotypes collected in geneticstudies. In such datasets we expect correlations between phenotypes and betweenindividuals. We model observations as a sum of two matrix normal variates suchthat the joint covariance function is a sum of Kronecker products. This model,which generalizes the Graphical Lasso, assumes observations are correlated dueto known genetic relationships and corrupted with non-independent noise. Wehave developed a computationally efficient EM algorithm to fit this model. Onsimulated datasets we illustrate substantially improved performance in networkreconstruction by allowing for a general noise distribution.

Network inference in matrix-variate Gaussian models with non-independent noise