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Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure

Publiceringsår: 1997
Språk: Engelska
Sidor: 75-100
Publikation/Tidskrift/Serie: Journal of Classification
Volym: 14
Dokumenttyp: Artikel i tidskrift
Förlag: Springer New York


A statistical approach to a posteriori blockmodeling for graphs

is proposed. The model assumes that the vertices of the graph are partitioned into two unknown blocks and that the probability of an edge between two vertices depends only on the blocks to which they belong.

Statistical procedures are derived for estimating the probabilities of edges

and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this

strategy is practical only for small graphs. A Bayesian estimator,

based on Gibbs sampling, is proposed. This estimator is practical also

for large graphs. When ML estimators are used, the block structure can be

predicted based on predictive likelihood. When Gibbs sampling is used,

the block structure can be predicted from posterior predictive probabilities.

A side result is that when the number of vertices tends to infinity while

the probabilities remain constant, the block structure can be recovered

correctly with probability tending to 1.


  • Probability Theory and Statistics
  • Colored graph
  • EM algorithm
  • Latent class model
  • Social networks
  • Gibbs sampling


  • ISSN: 1432-1343

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