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In this paper, the asymptotic performance of a recently proposed distributed inference framework, structured variational methods, is investigated. The authors first distinguish the intra- and inter-cluster inference algorithms as vertex and edge processes respectively. Their difference is illustrated, and convergence rate is derived for the intra-cluster inference procedure which is based on an edge process. Then, viewed as a mixed vertex-edge process, the overall performance of structured variational methods is characterized via the coupling approach. Tradeoff between complexity and performance of this algorithm is also addressed, which provides in-sights for network design and analysis.
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