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Estimating Stochastic Block Models in the Presence of Covariates

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  • Yuichi Kitamura
  • Louise Laage

Abstract

In the standard stochastic block model for networks, the probability of a connection between two nodes, often referred to as the edge probability, depends on the unobserved communities each of these nodes belongs to. We consider a flexible framework in which each edge probability, together with the probability of community assignment, are also impacted by observed covariates. We propose a computationally tractable two-step procedure to estimate the conditional edge probabilities as well as the community assignment probabilities. The first step relies on a spectral clustering algorithm applied to a localized adjacency matrix of the network. In the second step, k-nearest neighbor regression estimates are computed on the extracted communities. We study the statistical properties of these estimators by providing non-asymptotic bounds.

Suggested Citation

  • Yuichi Kitamura & Louise Laage, 2024. "Estimating Stochastic Block Models in the Presence of Covariates," Papers 2402.16322, arXiv.org.
    • Handle: RePEc:arx:papers:2402.16322
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    References listed on IDEAS

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    1. Greenberg, Spencer & Mohri, Mehryar, 2014. "Tight lower bound on the probability of a binomial exceeding its expectation," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 91-98.
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