On Graphical Models and Convex Geometry

06/27/2021

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by   Haim Bar, et al.

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We introduce a mixture-model of beta distributions to identify significant correlations among P predictors when P is large. The method relies on theorems in convex geometry, which we use to show how to control the error rate of edge detection in graphical models. Our `betaMix' method does not require any assumptions about the network structure, nor does it assume that the network is sparse. The results in this article hold for a wide class of data generating distributions that include light-tailed and heavy-tailed spherically symmetric distributions.