Marginal likelihoods for distributed estimation of graphical model parameters

This paper considers the estimation of graphical model parameters with distributed data collection and computation. We first discuss the use and limitations of well-known distributed methods for marginal inference in the context of parameter estimation. We then describe an alternative framework for distributed parameter estimation based on maximizing marginal likelihoods. Each node independently estimates local parameters through solving a low-dimensional convex optimization with data collected from its local neighborhood. The local estimates are then combined into a global estimate without iterative message-passing. We provide an asymptotic analysis of the proposed estimator, deriving in particular its rate of convergence. Numerical experiments validate the rate of convergence and demonstrate performance equivalent to the centralized maximum likelihood estimator.