Abstract

We investigate a curious relationship between the structure of a discrete graphical model and the support of the inverse of a generalized covariance matrix. We show that for certain graph structures, the support of the inverse covariance matrix of indicator variables on the vertices of a graph reflects the conditional independence structure of the graph. Our work extends results that have previously been established only in the context of multivariate Gaussian graphical models, thereby addressing an open question about the significance of the inverse covariance matrix of a non-Gaussian distribution. Based on our population-level results, we show how the graphical Lasso may be used to recover the edge structure of certain classes of discrete graphical models, and present simulations to verify our theoretical results.