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Variational Inference for Stochastic Block Models From Sampled Data

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  • Timothée Tabouy
  • Pierre Barbillon
  • Julien Chiquet

Abstract

This article deals with nonobserved dyads during the sampling of a network and consecutive issues in the inference of the stochastic block model (SBM). We review sampling designs and recover missing at random (MAR) and not missing at random (NMAR) conditions for the SBM. We introduce variants of the variational EM algorithm for inferring the SBM under various sampling designs (MAR and NMAR) all available as an R package. Model selection criteria based on integrated classification likelihood are derived for selecting both the number of blocks and the sampling design. We investigate the accuracy and the range of applicability of these algorithms with simulations. We explore two real-world networks from ethnology (seed circulation network) and biology (protein–protein interaction network), where the interpretations considerably depend on the sampling designs considered. Supplementary materials for this article are available online.

Suggested Citation

  • Timothée Tabouy & Pierre Barbillon & Julien Chiquet, 2020. "Variational Inference for Stochastic Block Models From Sampled Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(529), pages 455-466, January.
    • Handle: RePEc:taf:jnlasa:v:115:y:2020:i:529:p:455-466
    DOI: 10.1080/01621459.2018.1562934
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    Cited by:

    1. Marino, Maria Francesca & Pandolfi, Silvia, 2022. "Hybrid maximum likelihood inference for stochastic block models," Computational Statistics & Data Analysis, Elsevier, vol. 171(C).
    2. Gaucher, Solenne & Klopp, Olga & Robin, Geneviève, 2021. "Outlier detection in networks with missing links," Computational Statistics & Data Analysis, Elsevier, vol. 164(C).
    3. Saint‐Clair Chabert‐Liddell & Pierre Barbillon & Sophie Donnet, 2022. "Impact of the mesoscale structure of a bipartite ecological interaction network on its robustness through a probabilistic modeling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(2), March.

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