Distributed Covariance Estimation in Gaussian Graphical Models

—We consider distributed estimation of the inverse covariance matrix in Gaussian graphical models. These models factorize the multivariate distribution and allow for efficient distributed signal processing methods such as belief propagation (BP). The classical maximum likelihood approach to this covariance estimation problem, or potential function estimation in BP terminology, 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 local maximum likelihood estimator is asymptotically consistent but suboptimal, i.e., it does not minimize mean squared estimation (MSE) error. We propose to improve the MSE performance by introducing additional symmetry constraints using averaging and pseudolikelihood estimation approaches. We compute the proposed estimates using mess...

• Type: Journal
• Year: 2012
• Where: TSP
• Authors: Ami Wiesel, Alfred O. Hero
• Keywords: Artificial Intelligence, Maximum Likelihood Approach, Symmetry Constraints, TSP 2012, Wireless Sensor Network