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Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models

Author

Listed:
  • Sirio Legramanti

    (Bocconi University)

  • Tommaso Rigon

    (Duke University)

  • Daniele Durante

    (Bocconi University)

Abstract

Network data often exhibit block structures characterized by clusters of nodes with similar patterns of edge formation. When such relational data are complemented by additional information on exogenous node partitions, these sources of knowledge are typically included in the model to supervise the cluster assignment mechanism or to improve inference on edge probabilities. Although these solutions are routinely implemented, there is a lack of formal approaches to test if a given external node partition is in line with the endogenous clustering structure encoding stochastic equivalence patterns among the nodes in the network. To fill this gap, we develop a formal Bayesian testing procedure which relies on the calculation of the Bayes factor between a stochastic block model with known grouping structure defined by the exogenous node partition and an infinite relational model that allows the endogenous clustering configurations to be unknown, random and fully revealed by the block–connectivity patterns in the network. A simple Markov chain Monte Carlo method for computing the Bayes factor and quantifying uncertainty in the endogenous groups is proposed. This strategy is evaluated in simulations, and in applications studying brain networks of Alzheimer’s patients.

Suggested Citation

  • Sirio Legramanti & Tommaso Rigon & Daniele Durante, 2022. "Bayesian Testing for Exogenous Partition Structures in Stochastic Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 108-126, June.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-020-00231-2
    DOI: 10.1007/s13171-020-00231-2
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    References listed on IDEAS

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    1. D. S. Choi & P. J. Wolfe & E. M. Airoldi, 2012. "Stochastic blockmodels with a growing number of classes," Biometrika, Biometrika Trust, vol. 99(2), pages 273-284.
    2. M. E. J. Newman & Aaron Clauset, 2016. "Structure and inference in annotated networks," Nature Communications, Nature, vol. 7(1), pages 1-11, September.
    3. Nowicki K. & Snijders T. A. B., 2001. "Estimation and Prediction for Stochastic Blockstructures," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1077-1087, September.
    4. Prasenjit Ghosh & Debdeep Pati & Anirban Bhattacharya, 2020. "Posterior Contraction Rates for Stochastic Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 82(2), pages 448-476, August.
    5. Junxian Geng & Anirban Bhattacharya & Debdeep Pati, 2019. "Probabilistic Community Detection With Unknown Number of Communities," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(526), pages 893-905, April.
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