A likelihood ratio test for separability of covariances
Journal of Multivariate Analysis
The Journal of Machine Learning Research
Covariance selection for nonchordal graphs via chordal embedding
Optimization Methods & Software - Mathematical programming in data mining and machine learning
High Dimensional Inverse Covariance Matrix Estimation via Linear Programming
The Journal of Machine Learning Research
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Motivated by analysis of gene expression data measured over different tissues or over time, we consider matrix-valued random variable and matrix-normal distribution, where the precision matrices have a graphical interpretation for genes and tissues, respectively. We present a l"1 penalized likelihood method and an efficient coordinate descent-based computational algorithm for model selection and estimation in such matrix normal graphical models (MNGMs). We provide theoretical results on the asymptotic distributions, the rates of convergence of the estimates and the sparsistency, allowing both the numbers of genes and tissues to diverge as the sample size goes to infinity. Simulation results demonstrate that the MNGMs can lead to a better estimate of the precision matrices and better identifications of the graph structures than the standard Gaussian graphical models. We illustrate the methods with an analysis of mouse gene expression data measured over ten different tissues.