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Corrected Bayesian Information Criterion for Stochastic Block Models

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  • Jianwei Hu
  • Hong Qin
  • Ting Yan
  • Yunpeng Zhao

Abstract

Estimating the number of communities is one of the fundamental problems in community detection. We re-examine the Bayesian paradigm for stochastic block models (SBMs) and propose a “corrected Bayesian information criterion” (CBIC), to determine the number of communities and show that the proposed criterion is consistent under mild conditions as the size of the network and the number of communities go to infinity. The CBIC outperforms those used in Wang and Bickel and Saldana, Yu, and Feng which tend to underestimate and overestimate the number of communities, respectively. The results are further extended to degree corrected SBMs. Numerical studies demonstrate our theoretical results.

Suggested Citation

  • Jianwei Hu & Hong Qin & Ting Yan & Yunpeng Zhao, 2020. "Corrected Bayesian Information Criterion for Stochastic Block Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(532), pages 1771-1783, December.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:532:p:1771-1783
    DOI: 10.1080/01621459.2019.1637744
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    Cited by:

    1. Wu, Qianyong & Hu, Jiang, 2024. "Two-sample test of stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 192(C).
    2. Deng, Jiayi & Huang, Danyang & Ding, Yi & Zhu, Yingqiu & Jing, Bingyi & Zhang, Bo, 2024. "Subsampling spectral clustering for stochastic block models in large-scale networks," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    3. Mingyang Ren & Sanguo Zhang & Junhui Wang, 2023. "Consistent estimation of the number of communities via regularized network embedding," Biometrics, The International Biometric Society, vol. 79(3), pages 2404-2416, September.
    4. Vainora, J., 2024. "Latent Position-Based Modeling of Parameter Heterogeneity," Cambridge Working Papers in Economics 2455, Faculty of Economics, University of Cambridge.
    5. Ovielt Baltodano L'opez & Roberto Casarin, 2022. "A Dynamic Stochastic Block Model for Multi-Layer Networks," Papers 2209.09354, arXiv.org.

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