IDEAS home Printed from https://ideas.repec.org/a/spr/sankha/v84y2022i1d10.1007_s13171-020-00231-2.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13171-020-00231-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.

    File URL: https://libkey.io/10.1007/s13171-020-00231-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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. 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.
    3. 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.
    4. M. E. J. Newman & Aaron Clauset, 2016. "Structure and inference in annotated networks," Nature Communications, Nature, vol. 7(1), pages 1-11, September.
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. 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.
    3. 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.
    4. 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.
    5. Heather Mathews & Alexander Volfovsky, 2023. "Community informed experimental design," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 32(4), pages 1141-1166, October.
    6. Falk Bräuning & Siem Jan Koopman, 2016. "The dynamic factor network model with an application to global credit risk," Working Papers 16-13, Federal Reserve Bank of Boston.
    7. Zhou, Bin & Yan, Xiao-Yong & Xu, Xiao-Ke & Xu, Xiao-Ting & Wang, Nianxin, 2018. "Evolutionary of online social networks driven by pareto wealth distribution and bidirectional preferential attachment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 427-434.
    8. Leto Peel & Tiago P. Peixoto & Manlio De Domenico, 2022. "Statistical inference links data and theory in network science," Nature Communications, Nature, vol. 13(1), pages 1-15, December.
    9. Tom Britton, 2020. "Epidemic models on social networks—With inference," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 222-241, August.
    10. Cristiano Varin & Manuela Cattelan & David Firth, 2016. "Statistical modelling of citation exchange between statistics journals," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 179(1), pages 1-63, January.
    11. Thorben Funke & Till Becker, 2019. "Stochastic block models: A comparison of variants and inference methods," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-40, April.
    12. Ludkin, Matthew, 2020. "Inference for a generalised stochastic block model with unknown number of blocks and non-conjugate edge models," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    13. 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).
    14. Xiu Xu & Weining Wang & Yongcheol Shin & Chaowen Zheng, 2024. "Dynamic Network Quantile Regression Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 42(2), pages 407-421, April.
    15. 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.
    16. Jun Liu & Jiangzhou Wang & Binghui Liu, 2020. "Community Detection of Multi-Layer Attributed Networks via Penalized Alternating Factorization," Mathematics, MDPI, vol. 8(2), pages 1-20, February.
    17. Zhou, Bin & Xu, Xiao-Ting & Liu, Jian-Guo & Xu, Xiao-Ke & Wang, Nianxin, 2019. "Information interaction model for the mobile communication networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 1170-1176.
    18. Xu, Xiu & Wang, Weining & Shin, Yongcheol, 2020. "Dynamic Spatial Network Quantile Autoregression," IRTG 1792 Discussion Papers 2020-024, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    19. Arora, Saurabh & Sanditov, Bulat, 2009. "Caste as Community? Networks of social affinity in a South Indian village," MERIT Working Papers 2009-037, United Nations University - Maastricht Economic and Social Research Institute on Innovation and Technology (MERIT).
    20. Chang, Zhenhai & Yin, Xianjun & Jia, Caiyan & Wang, Xiaoyang, 2018. "Mixture models with entropy regularization for community detection in networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 339-350.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sankha:v:84:y:2022:i:1:d:10.1007_s13171-020-00231-2. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.