High dimensional Gaussian graphical models provide a rigorous framework to describe a network of statistical dependencies between variables, such as genes in genomic regulation studies or species in ecology. Penalized methods, including the standard Graphical-Lasso, are well-known approaches to infer the parameters of these models. As the number of variables in the model grow, the network inference and interpretation become more complex. The Normal-Block model is discussed, a model that clusters variables and considers a network at the cluster level. This both adds structure to the network and reduces the number of parameters at stake, thereby easing the inference and interpretation of the underlying network. The approach builds on Graphical-Lasso to add a penalty on the network’s edges and limit the detection of spurious dependencies. A zero-inflated version of the model is also proposed to account for real-world data properties. For the inference procedure, two approaches are introduced, a two-step method based on existing approaches and an original, more rigorous method that simultaneously infers the clustering of variables and the association network between clusters, using a penalized variational Expectation-Maximization approach. An implementation of the model in R, in a package called normalblockr, is available on github1. The results of the models in terms of clustering and network inference are presented, using both simulated data and various types of real-world data (proteomics and words occurrences on webpages).
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