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Tiago P Peixoto1

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A new merge-split algorithm efficiently samples network partitions using the stochastic block model (SBM). This method significantly improves sampling accuracy and speed compared to single-node approaches, even for hierarchical structures.

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Area of Science:

  • Network science
  • Statistical modeling
  • Computational statistics

Background:

  • The stochastic block model (SBM) is a fundamental tool for analyzing network community structure.
  • Accurate posterior inference of SBM partitions is computationally challenging.
  • Existing methods, like single-node moves, often suffer from poor mixing and sampling bias.

Purpose of the Study:

  • To develop an efficient Markov chain Monte Carlo (MCMC) scheme for SBM network partition inference.
  • To address the limitations of existing sampling methods in terms of accuracy and computational speed.
  • To extend the proposed method for analyzing hierarchical network structures.

Main Methods:

  • A novel MCMC scheme utilizing group merges and splits for sampling SBM partitions.
  • Comparative analysis of the merge-split approach against single-node move algorithms.
  • Extension of the merge-split scheme to nested stochastic block models.

Main Results:

  • The merge-split MCMC scheme demonstrates superior performance in sampling network partitions compared to single-node methods.
  • Significant improvements in Markov chain mixing times, often by several orders of magnitude.
  • Successful extension to nested SBMs, providing asymptotically exact samples of hierarchical partitions.

Conclusions:

  • The merge-split MCMC algorithm offers a highly efficient and accurate method for SBM inference.
  • This approach overcomes key limitations of traditional sampling techniques for network community detection.
  • The method provides a robust framework for analyzing complex hierarchical network structures.