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 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.
Bibliographical noteFunding Information:
Manuscript received January 23, 2011; revised July 14, 2011; accepted September 28, 2011. Date of publication October 18, 2011; date of current version December 16, 2011. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Roberto Lopez-Valcarce. This work was supported in part by by AFOSR grant FA9550-06-1-0324, and by a ISF grant 786/11. The work of A. Wiesel was supported by a Marie Curie Outgoing International Fellowship within the 7th European Community Framework Programme. The material in this paper was presented at the 6th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM-2010.
- Covariance estimation
- distributed signal processing
- graphical models