Distributed Covariance Estimation in

We consider distributed estimation of the inverse covariance matrix in Gaussian graphical models. These models factorize the multivariate distribution and allow for efficient dis- tributedsignalprocessingmethodssuchasbeliefpropagation(BP). The classical maximum likelihood approach to this covariance estimation problem, or potential function estimation in BP ter- minology, requires centralized computing and is computationally intensive. This motivates suboptimal distributed alternatives that tradeoff accuracy for communication cost. A natural solution is for each node to perform estimation of its local covariance with respect to its neighbors. The localmaximum likelihoodestimator is asymptotically consistent but suboptimal, i.e., it does not minimize mean squared estimation (MSE) error. We propose to improve the MSEperformancebyintroducingadditionalsymmetryconstraints using averaging and pseudolikelihood estimation approaches. We compute the proposed estimates using message passing protocols, which can be efficiently implemented in large scale graphical models with many nodes. We illustrate the advantages of our proposed methods using numerical experiments with synthetic data as well as real world data from a wireless sensor network.