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Convergence of Metropolis-Hastings Algorithm with Optimal Mixing Parameter in Bipartite Regular Graphs

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Software Engineering Perspectives in Systems (CSOC 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 501))

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Abstract

The Metropolis-Hastings algorithm, a multi-functional iterative procedure applicable in various technical/non-technical industries, has been attracting great attention of the scientific community since its definition. In this paper, we address the generalized Metropolis-Hastings algorithm for distributed averaging in bipartite regular graphs, where this algorithm with the optimal mixing parameter diverges. We identify that the convergence of the algorithm in bipartite regular graphs is achieved (in spite of the initial divergence), provided that a distributed mechanism for ensuring the convergence of the average consensus algorithm with the Maximum-degree weights in this mentioned critical graph topology is applied. Moreover, we examine in the paper how to reconfigure the algorithm the most efficiently after detecting a bipartite regular topology in a distributed way. The experimental part is concerned with the convergence rate of bounded Metropolis-Hastings algorithm with the optimal mixing parameter in bipartite regular graphs of various degrees when the mentioned mechanism with different rounding accuracy is used.

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Notes

  1. 1.

    determined by the vertex set V (v\(_i\) is the label of a vertex) and the edge set E (e\(_{ij}\) is the label of an edge linking v\(_i\) and v\(_j\)).

  2. 2.

    Definition of bipartite graphs.

  3. 3.

    Definition of regular graphs.

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Acknowledgment

This work was supported by the VEGA agency under the contract No. 2/0155/19 and by the project Cyber-Physical System for smart tele-monitoring and tele-medicine for patients with COVID-19 (BAS-SAS-21-03). Since 2019, Martin Kenyeres has been a holder of the Stefan Schwarz Supporting Fund.

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Authors and Affiliations

  1. Institute of Informatics, Slovak Academy of Sciences, Dubravska cesta 9, 845 07, Bratislava, Slovakia

    Martin Kenyeres

  2. Frequentis AG, Innovationsstraße 1, 1100, Vienna, Austria

    Jozef Kenyeres

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  1. Martin Kenyeres
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Correspondence to Martin Kenyeres .

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  1. Faculty of Applied Informatics, Tomas Bata University in Zlin, Zlin, Czech Republic

    Radek Silhavy

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Kenyeres, M., Kenyeres, J. (2022). Convergence of Metropolis-Hastings Algorithm with Optimal Mixing Parameter in Bipartite Regular Graphs. In: Silhavy, R. (eds) Software Engineering Perspectives in Systems. CSOC 2022. Lecture Notes in Networks and Systems, vol 501. Springer, Cham. https://doi.org/10.1007/978-3-031-09070-7_40

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