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Gaussian Belief Propagation (BP) algorithm is one of the most importantdistributed algorithms in signal processing and statistical learning involvingMarkov networks. It is well known that the algorithm correctly computesmarginal density functions from a high dimensional joint density function overa Markov network in a finite number of iterations when the underlying Gaussiangraph is acyclic. It is also known more recently that the algorithm producescorrect marginal means asymptotically for cyclic Gaussian graphs under thecondition of walk summability. This paper extends this convergence resultfurther by showing that the convergence is exponential under the walksummability condition, and provides a simple bound for the convergence rate.

On Convergence Rate of the Gaussian Belief Propagation Algorithm for Markov Networks