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Stochastic blockmodels with a growing number of classes

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  • D. S. Choi
  • P. J. Wolfe
  • E. M. Airoldi

Abstract

We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising self-reported school friendships, resulting in block estimates that reveal residual structure. Copyright 2012, Oxford University Press.

Suggested Citation

  • 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.
    • Handle: RePEc:oup:biomet:v:99:y:2012:i:2:p:273-284
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    File URL: http://hdl.handle.net/10.1093/biomet/asr053
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    Cited by:

    1. Yunpeng Zhao & Qing Pan & Chengan Du, 2019. "Logistic regression augmented community detection for network data with application in identifying autism‐related gene pathways," Biometrics, The International Biometric Society, vol. 75(1), pages 222-234, March.
    2. Lee, Kevin H. & Xue, Lingzhou & Hunter, David R., 2020. "Model-based clustering of time-evolving networks through temporal exponential-family random graph models," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    3. Thibaut Lamadon & Elena Manresa & Stephane Bonhomme, 2016. "Discretizing Unobserved Heterogeneity," 2016 Meeting Papers 1536, Society for Economic Dynamics.
    4. Fei Ma & Yixuan Wang & Kum Fai Yuen & Wenlin Wang & Xiaodan Li & Yuan Liang, 2019. "The Evolution of the Spatial Association Effect of Carbon Emissions in Transportation: A Social Network Perspective," IJERPH, MDPI, vol. 16(12), pages 1-23, June.
    5. Hric, Darko & Kaski, Kimmo & Kivelä, Mikko, 2018. "Stochastic block model reveals maps of citation patterns and their evolution in time," Journal of Informetrics, Elsevier, vol. 12(3), pages 757-783.
    6. Zhao, Yunpeng, 2020. "A note on new Bernstein-type inequalities for the log-likelihood function of Bernoulli variables," Statistics & Probability Letters, Elsevier, vol. 163(C).
    7. Dragana M. Pavlović & Bryan R.L. Guillaume & Soroosh Afyouni & Thomas E. Nichols, 2020. "Multi‐subject stochastic blockmodels with mixed effects for adaptive analysis of individual differences in human brain network cluster structure," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 363-396, August.
    8. Haiyan Liu & Ick Hoon Jin & Zhiyong Zhang & Ying Yuan, 2021. "Social Network Mediation Analysis: A Latent Space Approach," Psychometrika, Springer;The Psychometric Society, vol. 86(1), pages 272-298, March.
    9. Tin Lok James Ng & Thomas Brendan Murphy, 2021. "Weighted stochastic block model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(5), pages 1365-1398, December.
    10. 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.
    11. Tian, Yahui & Gel, Yulia R., 2019. "Fusing data depth with complex networks: Community detection with prior information," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 99-116.
    12. Zhang, Yue & Yuan, Mingao, 2020. "Nonreconstruction of high-dimensional stochastic block model with bounded degree," Statistics & Probability Letters, Elsevier, vol. 158(C).
    13. Babkin, Sergii & Stewart, Jonathan R. & Long, Xiaochen & Schweinberger, Michael, 2020. "Large-scale estimation of random graph models with local dependence," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    14. Olga Klopp & Nicolas Verzelen, 2017. "Optimal graphon estimation in cut distance," Working Papers 2017-42, Center for Research in Economics and Statistics.

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