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A semiparametric extension of the stochastic block model for longitudinal networks

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  • C Matias
  • T Rebafka
  • F Villers

Abstract

SummaryWe propose an extension of the stochastic block model for recurrent interaction events in continuous time, where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. We show that the model is identifiable and estimate it with a semiparametric variational expectation-maximization algorithm. We develop two versions of the method, one using a nonparametric histogram approach with an adaptive choice of the partition size, and the other using kernel intensity estimators. We select the number of latent groups by an integrated classification likelihood criterion. We demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach, and comment on competing methods.

Suggested Citation

  • C Matias & T Rebafka & F Villers, 2018. "A semiparametric extension of the stochastic block model for longitudinal networks," Biometrika, Biometrika Trust, vol. 105(3), pages 665-680.
    • Handle: RePEc:oup:biomet:v:105:y:2018:i:3:p:665-680.
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    File URL: http://hdl.handle.net/10.1093/biomet/asy016
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    References listed on IDEAS

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    1. Eric W. Fox & Martin B. Short & Frederic P. Schoenberg & Kathryn D. Coronges & Andrea L. Bertozzi, 2016. "Modeling E-mail Networks and Inferring Leadership Using Self-Exciting Point Processes," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 564-584, April.
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    5. Petter Holme, 2015. "Modern temporal network theory: a colloquium," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 88(9), pages 1-30, September.
    6. Robin, Stephane & Bar-Hen, Avner & Daudin, Jean-Jacques & Pierre, Laurent, 2007. "A semi-parametric approach for mixture models: Application to local false discovery rate estimation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5483-5493, August.
    7. Catherine Matias & Vincent Miele, 2017. "Statistical clustering of temporal networks through a dynamic stochastic block model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(4), pages 1119-1141, September.
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    Cited by:

    1. Hledik, Juraj & Rastelli, Riccardo, 2020. "A dynamic network model to measure exposure diversification in the Austrian interbank market," ESRB Working Paper Series 109, European Systemic Risk Board.
    2. Riccardo Rastelli & Michael Fop, 2020. "A stochastic block model for interaction lengths," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 14(2), pages 485-512, June.
    3. Yanqiao Zheng & Xiaobing Zhao & Xiaoqi Zhang & Xinyue Ye & Qiwen Dai, 2019. "Mining the Hidden Link Structure from Distribution Flows for a Spatial Social Network," Complexity, Hindawi, vol. 2019, pages 1-17, May.
    4. Paul Riverain & Simon Fossier & Mohamed Nadif, 2023. "Poisson degree corrected dynamic stochastic block model," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 135-162, March.
    5. Tom A.B. Snijders & Malick Faye & Julien Brailly, 2020. "Network dynamics with a nested node set: Sociability in seven villages in Senegal," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 74(3), pages 300-323, August.

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