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Stochastic blockmodels with a growing number of classes
Open accessAbstract
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.
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Citations
Cites
Modularity and community structure in networks
Newman, M. E. J. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0601602103 · Cited by 12,256
Cited by
Community Detection and Stochastic Block Models
Abbe, E. (2018) · now publishers, Inc. eBooks · doi:10.1561/9781680834772 · Cited by 544
Grouped Patterns of Heterogeneity in Panel Data
Bonhomme, S., & Manresa, E. (2015) · Econometrica · doi:10.3982/ecta11319 · Cited by 451
Metadata
- Authors
- Choi, D. S., Wolfe, P. J., & Airoldi, E. M.
- Venue
- Biometrika
- Publisher
- Oxford University Press (OUP)
- Published
- 2012-04-17
- Volume
- 99
- Issue
- 2
- Pages
- 273-284
- ISSN
- 0006-3444 (ISSN-L)
- 1464-3510
- OpenAlex
- W2111547480
- Cited by
- 220
- References
- 1
- FWCI
- 15.57
- Type
- journal article
- Language
- en
- Open access
- green
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- Choi, D. S., Wolfe, P. J., & Airoldi, E. M. (2012). Stochastic blockmodels with a growing number of classes. Biometrika. https://doi.org/10.1093/biomet/asr053
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