Estimation of symmetry-constrained Gaussian graphical models: application to clustered dense networks

We propose a model selection algorithm for high-dimensional clustered data. Our algorithm combines a classical penalized likelihood method with a composite likelihood approach in the framework of coloured graphical Gaussian models. Our method is designed to identify high-dimensional dense networks with a large number of edges but sparse edge classes. Its empirical performance is demonstrated through simulation studies and a network analysis of a gene expression dataset.