Walk-Sums and Belief Propagation in Gaussian Graphical Models
The Journal of Machine Learning Research
Factor graphs and the sum-product algorithm
IEEE Transactions on Information Theory
An analysis of belief propagation on the turbo decoding graph with Gaussian densities
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
Distributed large scale network utility maximization
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
A low density lattice decoder via non-parametric belief propagation
Allerton'09 Proceedings of the 47th annual Allerton conference on Communication, control, and computing
Properties of Bethe free energies and message passing in Gaussian models
Journal of Artificial Intelligence Research
Linear coordinate-descent message passing for quadratic optimization
Neural Computation
Message-passing algorithms for quadratic minimization
The Journal of Machine Learning Research
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Gaussian belief propagation (GaBP) is an iterative message-passing algorithm for inference in Gaussian graphical models. It is known that when GaBP converges it converges to the correct MAP estimate of the Gaussian random vector and simple sufficient conditions for its convergence have been established. In this paper we develop a double-loop algorithm for forcing convergence of GaBP. Our method computes the correct MAP estimate even in cases where standard GaBP would not have converged. We further extend this construction to compute least-squares solutions of over-constrained linear systems. We believe that our construction has numerous applications, since the GaBP algorithm is linked to solution of linear systems of equations, which is a fundamental problem in computer science and engineering. As a case study, we discuss the linear detection problem. We show that using our new construction, we are able to force convergence of Montanari's linear detection algorithm, in cases where it would originally fail. As a consequence, we are able to increase significantly the number of users that can transmit concurrently.