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Improved Bayesian inference for the stochastic block model with application to large networks


  • McDaid, Aaron F.
  • Murphy, Thomas Brendan
  • Friel, Nial
  • Hurley, Neil J.


An efficient MCMC algorithm is presented to cluster the nodes of a network such that nodes with similar role in the network are clustered together. This is known as block-modeling or block-clustering. The model is the stochastic blockmodel (SBM) with block parameters integrated out. The resulting marginal distribution defines a posterior over the number of clusters and cluster memberships. Sampling from this posterior is simpler than from the original SBM as transdimensional MCMC can be avoided. The algorithm is based on the allocation sampler. It requires a prior to be placed on the number of clusters, thereby allowing the number of clusters to be directly estimated by the algorithm, rather than being given as an input parameter. Synthetic and real data are used to test the speed and accuracy of the model and algorithm, including the ability to estimate the number of clusters. The algorithm can scale to networks with up to ten thousand nodes and tens of millions of edges.

Suggested Citation

  • McDaid, Aaron F. & Murphy, Thomas Brendan & Friel, Nial & Hurley, Neil J., 2013. "Improved Bayesian inference for the stochastic block model with application to large networks," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 12-31.
  • Handle: RePEc:eee:csdana:v:60:y:2013:i:c:p:12-31
    DOI: 10.1016/j.csda.2012.10.021

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    References listed on IDEAS

    1. Mark S. Handcock & Adrian E. Raftery & Jeremy M. Tantrum, 2007. "Model-based clustering for social networks," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 170(2), pages 301-354.
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    1. repec:spr:compst:v:32:y:2017:i:2:d:10.1007_s00180-016-0655-5 is not listed on IDEAS
    2. Marco Bertoletti & Nial Friel & Riccardo Rastelli, 2015. "Choosing the number of clusters in a finite mixture model using an exact integrated completed likelihood criterion," METRON, Springer;Sapienza Università di Roma, vol. 73(2), pages 177-199, August.


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