Stochastic blockmodels with a growing number of classes

• 成果类型: Article
• 署名作者: Choi, D. S.; Wolfe, P. J.; Airoldi, E. M.
• 署名单位: Harvard University; University of London; University College London; Harvard University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asr053
• 发表日期: 2012
• 页码: 273284
• 关键词: prediction; graphs; models

摘要

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.