Spectral Estimation of Large Stochastic Blockmodels with Discrete Nodal Covariates

Bibliographic Data

ID19418112
AuthorsAngelo Mele (0000-0003-2890-6042, Carey Business School, Johns Hopkins University, Baltimore, MD, corresponding author), Ling-Xin Hao (0000-0002-4694-0917, Johns Hopkins University), Lingxin Hao (Johns Hopkins University), Joshua Cape (0000-0002-1471-1650, University of Wisconsin–Madison), Carey E Priebe (0000-0002-0139-7201, Johns Hopkins University)
Year2023
Volume41
Issue4
Pages1364-1376
Publication date2023-10-02
Open AccessNo
TypeARTICLE
VenueJournal of Business and Economic Statistics (JOURNAL)
Journal identifiersISSN: 0735-0015 • E-ISSN: 1537-2707
PublisherInforma UK Limited (PUBLISHER • GB)
DOI10.1080/07350015.2022.2139709
OpenAlexW4307565332
LanguageEN
Citations received1
References cited36

In many applications of network analysis, it is important to distinguish between observed and unobserved factors affecting network structure. We show that a network model with discrete unobserved link heterogeneity and binary (or discrete) covariates corresponds to a stochastic blockmodel (SBM). We develop a spectral estimator for the effect of covariates on link probabilities, exploiting the correspondence of SBMs and generalized random dot product graphs (GRDPG). 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. Finally, we establish asymptotic normality of our estimators

Covariate · Econometrics · Economics · Estimation · Statistics · Bayesian Methods and Mixture Models · Mathematics · Random Matrices and Applications · Statistical Methods and Inference · Applied Mathematics

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