Variational Bayesian inference and complexity control for stochastic block models

Statistical Modelling

Volumn 12, Issue 1, 2012, Pages 93-115

  Latouche, P ^a   Birmele E ^a   Ambroise, C ^a  

^a University of Paris 5   (France)

Author keywords

community detection; integrated complete data likelihood; integrated observed data likelihood; random graphs; stochastic block models; variational Bayes EM; variational EM

Indexed keywords

EID: 84859344722     PISSN: 1471082X     EISSN: 14770342     Source Type: Journal    
DOI: 10.1177/1471082X1001200105     Document Type: Article

References (37)

1. Airoldi EM,Blei DM,Fienberg SE,Xing EP.Mixed-membership stochastic blockmodels.Journal of Machine Learning Research. 2008;9:1981-2014.
2. Albert R,Barabási AL.Statistical mechanics of complex networks.Modern Physics. 2002;74:47-97.
3. Allman ES,Matias C,Rhodes JA.Identifiability of parameters in latent structure models with many observed variables.Annals of Statistics. 2009;37:3099-132.
4. Attias HUncertainty in artificial intelligence: proceedings of the fifth conference. Laskey KBPrade H, ed. San Francisco, CA: Morgan Kaufmann; 1999:21-30.
5. Barabási A,Oltvai ZN.Network biology: understanding the cell's functional organization.Nature Review Genetics. 2004;5:101-13.
6. Biernacki C,Celeux G,Govaert G.Assessing a mixture model for clustering with the integrated completed likelihood.IEEE Transactions Pattern Analysis and Machine Inteligence. 2000;7:719-25.
7. Biernacki C,Celeux G,Govaert G.Exact and monte carlo calculations of integrated likelihoods for the latent class model.Journal of Statistical Planning and Inference. 2010;140:2991-3002.
8. Boer P,Huisman M,Snijders TAB,Steglich CEG,Wichers LHY,Zeggelink EPH.StOCNET: an open software system for the advanced statistical analysis of social networks. 2006;:.
9. Burnham KP,Anderson DRModel selection and multi-model inference: a practical information-theoric approach. Colorado State University: Springer-Verlag; 2004:.
10. Corduneanu A,Bishop CArtificial intelligence and statistics: proceedings of the eighth conference. Richardson TJaakkola T, ed. Morgan Kaufmann; 2001:27-34.
11. Danon L,Diaz-Guilera A,Duch J,Arenas A.Comparing community structure identification.Journal of Statistical Mechanics. 2005;:.
12. Daudin J,Picard F,Robin S.A mixture model for random graph.Statistics and Computing. 2008;18:1-36.
13. Dempster AP,Laird NM,Rubin DB.Maximum likelihood for incomplete data via the EM algorithm.Journal of the Royal Statistical Society, Series B. 1977;39:1-38.
14. Estrada E,Rodriguez-Velazquez JA.Spectral measures of bipartivity in complex networks.Physical Review E. 2005;72:.
15. Fienberg SE,Wasserman S.Categorical data analysis of single sociometric relations.Sociological Methodology. 1981;12:156-92.
16. Frank O,Harary F.Cluster inference by using transitivity indices in empirical graphs.Journal of the American Statistical Association. 1982;77:835-40.
17. Girvan M,Newman MEJ.Community structure in social and biological networks.Proceedings of the National Academy of Science. 2002;99:7821-826.
18. Handcock MS,Raftery AE,Tantrum JM.Model-based clustering for social networks.Journal of the Royal Statistical Society, Series A. 2007;170:1-22.
19. Hathaway RJ.Another interpretation of the EM algorithm for mixture distributions.Statistics & Probability Letters. 1986;4:53-56.
20. Hoff PD,Raftery AE,Handcock MS.Latent space approaches to social network analysis.Journal of the American Statistical Association. 2002;97:1090-098.
21. Hofman JM,Wiggins CH.A Bayesian approach to network modularity.Physical Review Letters. 2008;100:258701.
22. Holland P,Laskey KB,Leinhardt S.Stochastic blockmodels: some first steps.Social Networks. 1983;5:109-37.
23. Jeffreys H.An invariant form for the prior probability in estimations problems.Proceedings of the Royal Society of London. Series A. 1946;186:453-61.
24. Kemp C,Griffiths TL,Tenenbaum JBDiscovering latent classes in relational data. Massachusetts, USA: MIT; 2004:.
25. KrivitskyPNHandcockMS (2009) The latentnet package[Computer software manual] (Version 2.1-1).
26. Lacroix V,Fernandes CG,Sagot M-F.Motif search in graphs: Application to metabolic networks.Transactions in Computational Biology and Bioinformatics. 2006;3:360-68.
27. Mariadassou M,Robin S,Vacher C.Uncovering latent structure in valued graphs: a variational approach.Annals of Applied Statistics. 2010;4:715-42.
28. McLachlan G,Krishnan TThe EM algorithm and extensions. New York: John Wiley; 1997:.
29. Neal R,Hinton GLearning in graphical models. Jordan MI, ed. Dordrecht: Kluwer; 1998:.
30. Newman M,Leicht E.Mixture models and exploratory analysis in networks.PNAS. 2007;104:9564-569.
31. Nowicki K,Snijders TAB.Estimation and prediction for stochastic blockstructures.Journal of the American Statistical Association. 2001;96:1077-087.
32. Palla G,Barabási A-L,Vicsek T.Quantifying social group evolution.Nature. 2007;446:664-67.
33. Snijders TAB,Nowicki K.Estimation and prediction for stochastic block-structures for graphs with latent block structure.Journal of Classification. 1997;14:75-100.
34. Svensén M,Bishop C.Robust Bayesian mixture modelling.Neurocomputing. 2004;64:235-52.
35. Watts DJ,Strogatz SH.Collective dynamics of small-world networks.Nature. 1998;393:440-42.
36. White H,Boorman S,Breiger R.Social structure from multiple networks. I. Blockmodels of roles and positions.American Journal of Sociology. 1976;81:730-80.
37. Zanghi H,Ambroise C,Miele V.Fast online graph clustering via Erdös Renyi mixture.Pattern Recognition. 2008;41:3592-599.