Marginal Likelihoods for Distributed Parameter Estimation of Gaussian Graphical Models

摘要: We consider distributed estimation of the inverse co- variance matrix, also called concentration or precision in Gaussian graphical models. Traditional centralized often requires global inference covariance which can be computationally intensive large dimensions. Approximate in- ference based on message-passing algorithms, other hand, lead to unstable and biased loopy Here, we propose a general framework for maximum margina ll ikelihood (MML) approach. This approach compute sl ocal parameter estimates by maximizing marginal likelihoods defined with respect data col- lected from local neighborhoods. Due non-convexity MML problem, introduce solve convex relaxation. The are then combined into estimate without need iterative between proposed algorithm is naturally parallelizable computa- tionally efficient, thereby making it suitable high-dimensional problems. In classical regime where number variables fixed samplesincreases infinity, estimator shown asymptotically consistent improve monotonically as neighborhood size increases. scaling bothandincrease convergence rate true parameters derived seen comparable maximum-likelihood estimation. Extensive numerica le xperiments demonstrate improved performance two-hop version estimator, suffices almost close gap likelihood at reduced computational cost.