Stochastic blockmodel approximation of a graphon: Theory and consistent estimation

Advances in Neural Information Processing Systems

Volumn , Issue , 2013, Pages

  Airoldi, Edoardo M ^a   Costa, Thiago B ^a,b   Chan, Stanley H ^a,b  

^a HARVARD UNIVERSITY   (United States)

^b SEAS ^*  (United States)

Author keywords

[No Author keywords available]

Indexed keywords

STOCHASTIC SYSTEMS;

COMPUTATIONALLY EFFICIENT; CONSISTENT ESTIMATION; ESTIMATION ERRORS; NETWORK DATA; NETWORK MODELING; NON-PARAMETRIC; NONPARAMETRIC APPROACHES; STOCHASTIC BLOCK MODELS;

STOCHASTIC MODELS;

EID: 84899007980     PISSN: 10495258     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (30)

1. E.M. Airoldi, D.M. Blei, S.E. Fienberg, and E.P. Xing. Mixed-membership stochastic blockmodels. Journal of Machine Learning Research, 9:1981-2014, 2008.
2. D.J. Aldous. Representations for partially exchangeable arrays of random variables. Journal of Multivariate Analysis, 11:581-598, 1981.
3. H. Azari and E.M. Airoldi. Graphlet decomposition of a weighted network. Journal of Machine Learning Research, W&CP, 22:54-63, 2012.
4. P.J. Bickel and A. Chen. A nonparametric view of network models and Newman-Girvan and other modularities. Proc. Natl. Acad. Sci. USA, 106:21068-21073, 2009.
5. P.J. Bickel, A. Chen, and E. Levina. The method of moments and degree distributions for network models. Annals of Statistics, 39(5):2280-2301, 2011.
6. C. Borgs, J. Chayes, L. Lovász, V. T. Sós, B. Szegedy, and K. Vesztergombi. Graph limits and parameter testing. In Proc. ACM Symposium on Theory of Computing, pages 261-270, 2006.
7. A. Channarond, J. Daudin, and S. Robin. Classification and estimation in the Stochastic Blockmodel based on the empirical degrees. Electronic Journal of Statistics, 6:2574-2601, 2012.
8. S. Chatterjee. Matrix estimation by universal singular value thresholding. ArXiv:1212.1247. 2012.
9. D.S. Choi and P.J.Wolfe. Co-clustering separately exchangeable network data. ArXiv:1212.4093. 2012.
10. D.S. Choi, P.J. Wolfe, and E.M. Airoldi. Stochastic blockmodels with a growing number of classes. Biometrika, 99:273-284, 2012.
11. P. Diaconis and S. Janson. Graph limits and exchangeable random graphs. Rendiconti di Matematica e delle sue Applicazioni, Series VII, pages 33-61, 2008.
12. A. Goldenberg, A.X. Zheng, S.E. Fienberg, and E.M. Airoldi. A survey of statistical network models. Foundations and Trends in Machine Learning, 2:129-233, 2009.
13. P.D. Hoff. Modeling homophily and stochastic equivalence in symmetric relational data. In Neural Information Processing Systems (NIPS), volume 20, pages 657-664, 2008.
14. P.D. Hoff, A.E. Raftery, and M.S. Handcock. Latent space approaches to social network analysis. Journal of the American Statistical Association, 97(460):1090-1098, 2002.
15. D.N. Hoover. Relations on probability spaces and arrays of random variables. Preprint, Institute for Advanced Study, Princeton, NJ, 1979.
16. O. Kallenberg. On the representation theorem for exchangeable arrays. Journal of Multivariate Analysis, 30(1):137-154, 1989.
17. R.H. Keshavan, A.Montanari, and S. Oh. Matrix completion from a few entries. IEEE Trans. Information Theory, 56:2980-2998, Jun. 2010.
18. N.D. Lawrence. Probabilistic non-linear principal component analysis with Gaussian process latent variable models. Journal of Machine Learning Research, 6:1783-1816, 2005.
19. J.R. Lloyd, P. Orbanz, Z. Ghahramani, and D.M. Roy. Random function priors for exchangeable arrays with applications to graphs and relational data. In Neural Information Processing Systems (NIPS), 2012.
20. L. Lovász and B. Szegedy. Limits of dense graph sequences. Journal of Combinatorial Theory, Series B, 96:933-957, 2006.
21. K.T. Miller, T.L. Griffiths, and M.I. Jordan. Nonparametric latent fature models for link prediction. In Neural Information Processing Systems (NIPS), 2009.
22. K. Nowicki and T.A. Snijders. Estimation and prediction of stochastic block structures. Journal of American Statistical Association, 96:1077-1087, 2001.
23. P. Orbanz and D.M. Roy. Bayesian models of graphs, arrays and other exchangeable random structures, 2013. Unpublished manuscript.
24. P.Latouche and S. Robin. Bayesian model averaging of stochastic block models to estimate the graphon function and motif frequencies in a w-graph model. ArXiv:1310.6150, October 2013. Unpublished manuscript.
25. K. Rohe, S. Chatterjee, and B. Yu. Spectral clustering and the high-dimensional stochastic blockmodel. Annals of Statistics, 39(4):1878-1915, 2011.
26. M. Tang, D.L. Sussman, and C.E. Priebe. Universally consistent vertex classification for latent positions graphs. Annals of Statistics, 2013. In press.
27. L. Wasserman. All of Nonparametric Statistics. Springer, 2005.
28. P.J. Wolfe and S.C. Olhede. Nonparametric graphon estimation. ArXiv:1309.5936, September 2013. Unpublished manuscript.
29. Z. Xu, F. Yan, and Y. Qi. Infinite Tucker decomposition: nonparametric Bayesian models for multiway data analysis. In Proc. Intl. Conf. Machine Learning (ICML), 2012.
30. Y. Zhao, E. Levina, and J. Zhu. Community extraction for social networks. In Proc. Natl. Acad. Sci. USA, volume 108, pages 7321-7326, 2011.