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

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