Abstract:
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Graphical models are central to machine learning and multivariate statistics. The number of parameters in these models grows at a super exponential rate in the number of nodes. The literature mainly focuses on cases where the graph is very sparse and consistent estimation is possible at the ratio of sample size to number of parameters typically encountered. In many application areas, such as genetics, epidemiology, and neuroscience, these extreme sparsity conditions are considered scientifically unrealistic. In these cases, a more realistic model is one in which the joint distribution of the data can be explained by a much lower-dimensional latent graph, or what in machine learning is referred to as a deep network. Here we propose a fully Bayesian approach to inference on latent graph structure that uses a nonparametric model of dependence between latent nodes. Some theoretical properties of the model are derived, and the model is applied to learning the dependence structure between scientifically meaningful groups of variables from a genetic epidemiological study and an electrophysiology dataset.
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