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The Hierarchy of Block Models

Author

Listed:
  • Majid Noroozi

    (Washington University in St. Louis)

  • Marianna Pensky

    (University of Central Florida)

Abstract

There exist various types of network block models such as the Stochastic Block Model (SBM), the Degree Corrected Block Model (DCBM), and the Popularity Adjusted Block Model (PABM). While this leads to a variety of choices, the block models do not have a nested structure. In addition, there is a substantial jump in the number of parameters from the DCBM to the PABM. The objective of this paper is formulation of a hierarchy of block model which does not rely on arbitrary identifiability conditions. We propose a Nested Block Model (NBM) that treats the SBM, the DCBM and the PABM as its particular cases with specific parameter values, and, in addition, allows a multitude of versions that are more complicated than DCBM but have fewer unknown parameters than the PABM. The latter allows one to carry out clustering and estimation without preliminary testing, to see which block model is really true.

Suggested Citation

  • Majid Noroozi & Marianna Pensky, 2022. "The Hierarchy of Block Models," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(1), pages 64-107, June.
    • Handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-021-00247-2
    DOI: 10.1007/s13171-021-00247-2
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    References listed on IDEAS

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    1. Srijan Sengupta & Yuguo Chen, 2018. "A block model for node popularity in networks with community structure," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 80(2), pages 365-386, March.
    2. P. Tseng, 2000. "Nearest q-Flat to m Points," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 249-252, April.
    3. Majid Noroozi & Ramchandra Rimal & Marianna Pensky, 2021. "Estimation and clustering in popularity adjusted block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 83(2), pages 293-317, April.
    4. Bo Wang & Armin Pourshafeie & Marinka Zitnik & Junjie Zhu & Carlos D. Bustamante & Serafim Batzoglou & Jure Leskovec, 2018. "Network enhancement as a general method to denoise weighted biological networks," Nature Communications, Nature, vol. 9(1), pages 1-8, December.
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    Cited by:

    1. Noroozi, Majid & Pensky, Marianna, 2024. "Sparse subspace clustering in diverse multiplex network model," Journal of Multivariate Analysis, Elsevier, vol. 203(C).

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