Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure |
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Authors: | Tom AB Snijders Krzysztof Nowicki |
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Institution: | (1) Department of Statistics and Measurement Theory, University of Groningen,;(2) Department of Statistics, University of Lund, |
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Abstract: | 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 the 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. |
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Keywords: | |
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