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Stochastic blockmodels with a growing number of classes. (English) Zbl 1318.62207
Summary: We present asymptotic and finite-sample results on the use of stochastic blockmodels for the analysis of network data. We show that the fraction of misclassified network nodes converges in probability to zero under maximum likelihood fitting when the number of classes is allowed to grow as the root of the network size and the average network degree grows at least poly-logarithmically in this size. We also establish finite-sample confidence bounds on maximum-likelihood blockmodel parameter estimates from data comprising independent Bernoulli random variates; these results hold uniformly over class assignment. We provide simulations verifying the conditions sufficient for our results, and conclude by fitting a logit parameterization of a stochastic blockmodel with covariates to a network data example comprising self-reported school friendships, resulting in block estimates that reveal residual structure.

MSC:
62H30 Classification and discrimination; cluster analysis (statistical aspects)
05C80 Random graphs (graph-theoretic aspects)
62P25 Applications of statistics to social sciences
91D30 Social networks; opinion dynamics
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