Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure
(1997) In Journal of Classification 14. p.75100 Abstract
 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... (More)  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. (Less)
Please use this url to cite or link to this publication:
http://lup.lub.lu.se/record/1767796
 author
 Snijders, Tom A. B. and Nowicki, Krzysztof ^{LU}
 organization
 publishing date
 1997
 type
 Contribution to journal
 publication status
 published
 subject
 keywords
 Colored graph, EM algorithm, Latent class model, Social networks, Gibbs sampling
 in
 Journal of Classification
 volume
 14
 pages
 75  100
 publisher
 Springer New York
 external identifiers

 scopus:0031495186
 ISSN
 14321343
 DOI
 10.1007/s003579900004
 language
 English
 LU publication?
 yes
 id
 ea745206a48e4a61a3d9fdb43967a910 (old id 1767796)
 date added to LUP
 20110127 14:50:33
 date last changed
 20170806 04:47:11
@article{ea745206a48e4a61a3d9fdb43967a910, abstract = {A statistical approach to a posteriori blockmodeling for graphs<br/><br> 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.<br/><br> Statistical procedures are derived for estimating the probabilities of edges<br/><br> and for predicting the block structure from observations of the edge pattern only. ML estimators can be computed using the EM algorithm, but this<br/><br> strategy is practical only for small graphs. A Bayesian estimator,<br/><br> based on Gibbs sampling, is proposed. This estimator is practical also<br/><br> for large graphs. When ML estimators are used, the block structure can be<br/><br> predicted based on predictive likelihood. When Gibbs sampling is used,<br/><br> the block structure can be predicted from posterior predictive probabilities.<br/><br> <br/><br> A side result is that when the number of vertices tends to infinity while<br/><br> the probabilities remain constant, the block structure can be recovered<br/><br> correctly with probability tending to 1.}, author = {Snijders, Tom A. B. and Nowicki, Krzysztof}, issn = {14321343}, keyword = {Colored graph,EM algorithm,Latent class model,Social networks,Gibbs sampling}, language = {eng}, pages = {75100}, publisher = {Springer New York}, series = {Journal of Classification}, title = {Estimation and Prediction for Stochastic Blockmodels for Graphs with Latent Block Structure}, url = {http://dx.doi.org/10.1007/s003579900004}, volume = {14}, year = {1997}, }