Distributed Learning of Gaussian Graphical Models via Marginal Likelihoods

摘要: We consider distributed estimation of the inverse covariance matrix, also called concentration in Gaussian graphical models. Traditional centralized often requires iterative and expensive global inference is therefore difficult large networks. In this paper, we propose a general framework for based on maximum marginal likelihood (MML) approach. Each node independently computes local estimate by maximizing defined with respect to data collected from its neighborhood. Due non-convexity MML problem, derive solving convex relaxation. The estimates are then combined into without need message-passing between neighborhoods. prove that relaxed estimator asymptotically consistent. Through numerical experiments several synthetic real-world sets, demonstrate two-hop version proposed significantly better than one-hop version, nearly closes gap many situations.