8 research outputs found
Convergence analysis of the information matrix in Gaussian belief propagation
Gaussian belief propagation (BP) has been widely used for distributed
estimation in large-scale networks such as the smart grid, communication
networks, and social networks, where local measurements/observations are
scattered over a wide geographical area. However, the convergence of Gaus- sian
BP is still an open issue. In this paper, we consider the convergence of
Gaussian BP, focusing in particular on the convergence of the information
matrix. We show analytically that the exchanged message information matrix
converges for arbitrary positive semidefinite initial value, and its dis- tance
to the unique positive definite limit matrix decreases exponentially fast.Comment: arXiv admin note: substantial text overlap with arXiv:1611.0201
Distributed Convergence Verification for Gaussian Belief Propagation
Gaussian belief propagation (BP) is a computationally efficient method to
approximate the marginal distribution and has been widely used for inference
with high dimensional data as well as distributed estimation in large-scale
networks. However, the convergence of Gaussian BP is still an open issue.
Though sufficient convergence conditions have been studied in the literature,
verifying these conditions requires gathering all the information over the
whole network, which defeats the main advantage of distributed computing by
using Gaussian BP. In this paper, we propose a novel sufficient convergence
condition for Gaussian BP that applies to both the pairwise linear Gaussian
model and to Gaussian Markov random fields. We show analytically that this
sufficient convergence condition can be easily verified in a distributed way
that satisfies the network topology constraint.Comment: accepted by Asilomar Conference on Signals, Systems, and Computers,
2017, Asilomar, Pacific Grove, CA. arXiv admin note: text overlap with
arXiv:1706.0407