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Estimation and Prediction for Stochastic Blockstructures
Abstract
A statistical approach to a posteriori blockmodeling for digraphs and valued digraphs is proposed. The probability model assumes that the vertices of the digraph are partitioned into several unobserved (latent) classes and that the probability distribution of the relation between two vertices depends only on the classes to which they belong. A Bayesian estimator based on Gibbs sampling is proposed. The basic model is not identified, because class labels are arbitrary. The resulting identifiability problems are solved by restricting inference to the posterior distributions of invariant functions of the parameters and the vertex class membership. In addition, models are considered where class labels are identified by prior distributions for the class membership of some of the vertices. The model is illustrated by an example from the social networks literature (Kapferer's tailor shop).
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Gelman, A., Carlin, J. B., Stern, H. S., & Rubin, D. B. (2003) · doi:10.1201/9780429258480 · Cited by 27,276
Social Structure from Multiple Networks. II. Role Structures
Boorman, S. A., & White, H. C. (1976) · American Journal of Sociology · doi:10.1086/226228 · Cited by 788
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Fortunato, S. (2010) · Physics Reports · doi:10.1016/j.physrep.2009.11.002 · Cited by 11,293
The political blogosphere and the 2004 U.S. election: divided they blog
Adamic, L. A., & Glance, N. (2005) · Proceedings of the 3rd international workshop on Link discovery · doi:10.1145/1134271.1134277 · Cited by 2,619
Latent Space Approaches to Social Network Analysis
Hoff, P. D., Raftery, A. E., & Handcock, M. S. (2002) · Journal of the American Statistical Association · doi:10.1198/016214502388618906 · Cited by 1,917
A Survey of Statistical Network Models
Goldenberg, A., Zheng, A. X., Fienberg, S. E., & Airoldi, E. M. (2010) · Foundations and Trends® in Machine Learning · doi:10.1561/2200000005 · Cited by 819
Relational learning via latent social dimensions
Tang, L., & Liu, H. (2009) · Proceedings of the 15th ACM SIGKDD international conference on Knowledge discovery and data mining · doi:10.1145/1557019.1557109 · Cited by 799
Metadata
- Authors
- Nowicki, K., & Snijders, T. A. B.
- Venue
- Journal of the American Statistical Association
- Publisher
- Informa UK Limited
- Published
- 2001-09
- Volume
- 96
- Issue
- 455
- Pages
- 1077-1087
- ISSN
- 0162-1459 (ISSN-L)
- 1537-274X
- OpenAlex
- W2144799688
- Cited by
- 1,148
- References
- 2
- FWCI
- 3.71
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
