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Volume 7 Issue 3
Apr.  2020

IEEE/CAA Journal of Automatica Sinica

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Article Navigation >  IEEE/CAA Journal of Automatica Sinica  > 2020  >  7(3): 668-673
Zhaorong Zhang and Minyue Fu, "Convergence Rate Analysis of Gaussian Belief Propagation for Markov Networks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 668-673, May 2020. doi: 10.1109/JAS.2020.1003105
Citation: Zhaorong Zhang and Minyue Fu, "Convergence Rate Analysis of Gaussian Belief Propagation for Markov Networks," IEEE/CAA J. Autom. Sinica, vol. 7, no. 3, pp. 668-673, May 2020. doi: 10.1109/JAS.2020.1003105
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Convergence Rate Analysis of Gaussian Belief Propagation for Markov Networks

doi: 10.1109/JAS.2020.1003105
  • 1.

    School of Electrical Engineering and Computer Science, The University of Newcastle. University Drive, NSW 2308, Australia

  • 2.

    School of Automation, Guangdong University of Technology, and Guangdong Key Laboratory of Intelligent Decision and Cooperative Control, Guangzhou 510006, China

Funds:  This work was supported by the National Natural Science Foundation of China (61633014, 61803101, U1701264)
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    Abstract
  • Gaussian belief propagation algorithm (GaBP) is one of the most important distributed algorithms in signal processing and statistical learning involving Markov networks. It is well known that the algorithm correctly computes marginal density functions from a high dimensional joint density function over a Markov network in a finite number of iterations when the underlying Gaussian graph is acyclic. It is also known more recently that the algorithm produces correct marginal means asymptotically for cyclic Gaussian graphs under the condition of walk summability (or generalised diagonal dominance). This paper extends this convergence result further by showing that the convergence is exponential under the generalised diagonal dominance condition, and provides a simple bound for the convergence rate. Our results are derived by combining the known walk summability approach for asymptotic convergence analysis with the control systems approach for stability analysis.

     

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    Highlights

    • A new bound on the convergence rate of the algorithm under the generalised diagonal dominance condition.
    • Theoretical development is done by combining the known walk summability approach for asymptotic convergence analysis with the control systems approach for stability analysis.
    • The work allows more application of the Gaussian Belief Propagation algorithm in distributed estimation and distributed optimisation.

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