Gaussian belief with dynamic data and in dynamic networkE. Aurell1, 2 and R. Pfitzner1, 3
1 KTH Linnaeus Centre ACCESS, KTH-Royal Institute of Technology - Stockholm, Sweden, EU
2 Department of Information and Computer Science, TKK-Helsinki University of Technology - Espoo, Finland, EU
3 Friedrich-Schiller-University Jena - Germany, EU
received 1 July 2009; accepted in final form 14 September 2009; published September 2009
published online 9 October 2009
In this paper we analyze Belief Propagation over a Gaussian model in a dynamic environment. Recently, this has been proposed as a method to average local measurement values by a distributed protocol (Consensus Propagation, MOALLEMI C. C. and VAN ROY B., IEEE Trans. Inf. Theory, 52 (2006) 4753) where the average is available for read-out at every single node. In the case that the underlying network is constant but the values to be averaged fluctuate (“dynamic data”), convergence and accuracy are determined by the spectral properties of an associated Ruelle-Perron-Frobenius operator. For Gaussian models on Erdős-Rényi graphs, numerical computation points to a spectral gap remaining in the large-size limit, implying exceptionally good scalability. In a model where the underlying network also fluctuates (“dynamic network”), averaging is more effective than in the dynamic data case. Altogether, this implies very good performance of these methods in very large systems, and opens a new field of statistical physics of large (and dynamic) information systems.
89.90.+n - Other topics in areas of applied and interdisciplinary physics.
89.20.Ff - Computer science and technology.
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