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Posterior Contraction Rates for Stochastic Block Models

Author

Listed:
  • Prasenjit Ghosh

    (Texas A&M University)

  • Debdeep Pati

    (Texas A&M University)

  • Anirban Bhattacharya

    (Texas A&M University)

Abstract

With the advent of structured data in the form of social networks, genetic circuits and protein interaction networks, statistical analysis of networks has gained popularity over recent years. The stochastic block model constitutes a classical cluster-exhibiting random graph model for networks. There is a substantial amount of literature devoted to proposing strategies for estimating and inferring parameters of the model, both from classical and Bayesian viewpoints. Unlike the classical counterpart, there is a dearth of theoretical results on the accuracy of estimation in the Bayesian setting. In this article, we undertake a theoretical investigation of the posterior distribution of the parameters in a stochastic block model. In particular, we show that one obtains near-optimal rates of posterior contraction with routinely used multinomial-Dirichlet priors on cluster indicators and uniform or general Beta priors on the probabilities of the random edge indicators. Our theoretical results are corroborated through a small scale simulation study.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:sankha:v:82:y:2020:i:2:d:10.1007_s13171-019-00180-5
    DOI: 10.1007/s13171-019-00180-5
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    References listed on IDEAS

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    1. 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.
    2. A. Golightly & D. J. Wilkinson, 2005. "Bayesian Inference for Stochastic Kinetic Models Using a Diffusion Approximation," Biometrics, The International Biometric Society, vol. 61(3), pages 781-788, September.
    3. repec:dau:papers:123456789/4648 is not listed on IDEAS
    4. Hoff P.D. & Raftery A.E. & Handcock M.S., 2002. "Latent Space Approaches to Social Network Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1090-1098, December.
    5. 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.
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    Cited by:

    1. 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.

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