Accuracy of variational estimates for random graph mixture models

Journal of Statistical Computation and Simulation

Volumn 82, Issue 6, 2012, Pages 849-862

  Gazal, Steven ^a   Daudin, Jean Jacques ^a   Robin, Stéphane ^a  

^a AgroParisTech   (France)

Author keywords

mixture model; random graph model; stochastic block model; variational Bayes inference; variational inference

Indexed keywords

EID: 84861445146     PISSN: 00949655     EISSN: 15635163     Source Type: Journal    
DOI: 10.1080/00949655.2011.560117     Document Type: Article

References (26)

1. Jordan, M. I., Ghahramani, Z., Jaakkola, T. and Saul, L. K. 1999. An introduction to variational methods for graphical models. 37(2): 183-233.
2. Jaakkola, T. S. 2000. Tutorial on variational approximation methods, Cambridge: MIT Press.
3. Dempster, A. P., Laird, N. M. and Rubin, D. B. 1977. Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc., B 39: 1-38.
4. Beal, M. J. and Ghahramani, Z. 2003. The variational Bayesian EM algorithm for incomplete data with application to scoring graphical model structures, Bayesian Statistics, Vol. 7, 543-552. Oxford: Oxford University Press.
5. Gunawardana, A. and Byrne, W. 2005. Convergence theorems for generalized alternating minimization procedures. J. Mach. Learn. Res., 6: 2049-2073.
6. McGrory, C. A. and Titterington, D. M. 2007. Variational approximations in Bayesian model selection for finite mixture distributions. Comput. Statist. Data Anal., 51: 5332-5367.
7. McGrory, C. A. and Titterington, D. M. 2009. Variational Bayesian analysis for hidden Markov models. Austral. NZ J. Statist., 51(2): 227-244.
8. Besag, J. 1986. On the statistical analysis of dirty pictures. J. R. Statist. Soc., B 48(3): 259-302.
9. Pattison, P. E. and Robins, G. L. 2008. "Probabilistic network theory". In Handbook of Probability Theory and Applications, New York: Sage Publication.
10. Nowicki, K. and Snijders, T. 2001. Estimation and prediction for stochastic block-structures. J. Amer. Statist. Assoc., 96: 1077-1087.
11. Daudin, J.-J., Picard, F. and Robin, S. 2008. A mixture model for random graphs. Statist. Comput., 18: 173-183.
12. Mariadassou, M., Robin, S. and Vacher, C. 2010. Uncovering structure in valued graphs: A variational approach. Ann. Appl. Statist., 4(2): 715-742.
13. Latouche, P., Birmelé, E. and Ambroise, C. 2008. "Bayesian methods for graph clustering". In SSB Research Report 17
14. Hofman, J. M. and Wiggins, C. H. 2008. Bayesian approach to network modularity. Phys. Rev. Lett., 100: 258701
15. Xu, Z., Tresp, V., Yu, S., Yu, K. and Kriegel, H.-P. 2007. Fast inference in infinite hidden relational models mlg07.dsi.unifi.it/pdf/27_Zhao_Zu.pdf
16. Picard, F., Miele, V., Daudin, J. J., Cottret, L. and Robin, S. 2009. Deciphering the connectivity structure of biological networks using MixNet. BMC Bioinformatics, 10: 1-11. doi:10.1186/1471-2105-10-S6-S17
17. Lauritzen, S. 1996. Graphical Models, Oxford Statistical Science Series Oxford: Clarendon Press.
18. Wainwright, M. J. and Jordan, M. I. 2008. Graphical models, exponential families, and variational inference. Found. Trends Mach. Learn., 1(1-2): 1-305. http:/dx.doi.org/10.1561/2200000001
19. McLachlan, G. and Peel, D. 2000. Finite mixture models, New York: Wiley.
20. MacKay, D. J. 2003. Information Theory, Inference, and Learning Algorithms, Cambridge: Cambridge University Press.
21. Winn, J. M. and Bishop, C. 2005. Variational message passing. J. Mach. Learn. Res., 6: 661-694.
22. Yedidia, J. S., Freeman, W. T. and Weiss, Y. 2003. "Understanding belief propagation and its generalizations". In Exploring Artificial Intelligence in the New Millenium, Edited by: Lakemeyer, G. and Netel, B. 239-236. San Francisco, CA: Morgan Kauffman.
23. Opper, M. and Winther, O. 2001. "From naive mean field theory to the TAP equations". In Advanced Mean Field Methods: Theory and Practice, Cambridge, MA: The MIT Press.
24. Balazsi, G., Barabasi, A.-L. and Oltvai, Z. 2005. Topological units of environmental signal processing in the transcriptional network of escherichia coli. Proc. Natl Acad. Sci., 102(22): 7841-7846.
25. Shen-Orr, S., Milo, R., Mangan, S. and Alon, U. 2002. Network motifs in the transcriptional regulation network of Escherichia coli. Nat. Genet., 31: 64-68.
26. Lancichinetti, A. and Fortunato, S. 2009. Community detection algorithms: A comparative analysis. Phys. Rev., E 80(5): 056117