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Spectral inference for large Stochastic Blockmodels with nodal covariates

Author

Listed:
  • Angelo Mele
  • Lingxin Hao
  • Joshua Cape
  • Carey E. Priebe

Abstract

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. To this end, we develop spectral estimators for both unobserved blocks and the effect of covariates in stochastic blockmodels. On the theoretical side, we establish asymptotic normality of our estimators for the subsequent purpose of performing inference. On the applied side, we show that computing our estimator is much faster than standard variational expectation--maximization algorithms and scales well for large networks. Monte Carlo experiments suggest that the estimator performs well under different data generating processes. Our application to Facebook data shows evidence of homophily in gender, role and campus-residence, while allowing us to discover unobserved communities. The results in this paper provide a foundation for spectral estimation of the effect of observed covariates as well as unobserved latent community structure on the probability of link formation in networks.

Suggested Citation

  • Angelo Mele & Lingxin Hao & Joshua Cape & Carey E. Priebe, 2019. "Spectral inference for large Stochastic Blockmodels with nodal covariates," Papers 1908.06438, arXiv.org, revised Mar 2021.
  • Handle: RePEc:arx:papers:1908.06438
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    File URL: http://arxiv.org/pdf/1908.06438
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    References listed on IDEAS

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    1. Paul Goldsmith-Pinkham & Guido W. Imbens, 2013. "Social Networks and the Identification of Peer Effects," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 253-264, July.
    2. Zhu, Mu & Ghodsi, Ali, 2006. "Automatic dimensionality selection from the scree plot via the use of profile likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 918-930, November.
    3. Eric Auerbach, 2019. "Identification and Estimation of a Partially Linear Regression Model using Network Data," Papers 1903.09679, arXiv.org, revised Jun 2021.
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    Cited by:

    1. Juan Nelson Mart'inez Dahbura & Shota Komatsu & Takanori Nishida & Angelo Mele, 2021. "A Structural Model of Business Card Exchange Networks," Papers 2105.12704, arXiv.org, revised Aug 2021.

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