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Article

Estimation in a binomial stochastic blockmodel for a weighted graph by a variational expectation maximization algorithm

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Pages 4450-4469 | Received 08 Feb 2019, Accepted 11 Mar 2020, Published online: 07 May 2020

References

  • Aicher, C., A. Z. Jacobs, and A. Clauset. 2013. Adapting the stochastic block model to edge-weighted networks. arXiv preprint arXiv:1305.5782.
  • Aicher, C., A. Z. Jacobs, and A. Clauset. 2015. Learning latent block structure in weighted networks. Journal of Complex Networks 3 (2):221–48. doi:10.1093/comnet/cnu026.
  • Airoldi, E., D. Blei, S. Fienberg, and E. Xing. 2008. Mixed membership stochastic blockmodels. The Journal of Machine Learning Research 9:1981–2014.
  • Anderson, C. J., S. Wasserman, and K. Faust. 1992. Building stochastic blockmodels. Social Networks 14 (1-2):137–61. doi:10.1016/0378-8733(92)90017-2.
  • Ball, B., B. Karrer, and M. E. Newman. 2011. Efficient and principled method for detecting communities in networks. Physical Review E 84 (3):036–103. doi:10.1103/PhysRevE.84.036103.
  • Biernacki, C., G. Celeux, and G. Govaert. 2000. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence 22 (7):719–25. doi:10.1109/34.865189.
  • Blei, D. M., A. Kucukelbir, and J. D. McAuliffe. 2017. Variational inference: A review for statisticians. Journal of the American Statistical Association 112 (518):859–77. doi:10.1080/01621459.2017.1285773.
  • Breiger, R. L. 1974. The duality of persons and groups. Social Forces 53 (2):181–90. doi:10.2307/2576011.
  • Celisse, A., J. J. Daudin, and L. Pierre. 2012. Consistency of maximum-likelihood and variational estimators in the stochastic block model. Electronic Journal of Statistics 6 (0):1847–99. doi:10.1214/12-EJS729.
  • Daudin, J., F. Picard, and S. Robin. 2008. A mixture model for random graph. Statistics and Computing 18 (2):173–36. doi:10.1007/s11222-007-9046-7.
  • Davies, A., B. B. Gardner, and M. R. Gardner. 1941. Deep South, Chicago: The University of Chicago Press.
  • Dempster, A. P., N. M. Laird, and D. B. Rubin. 1977. Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B (Methodological) 39 (1):1–38. doi:10.1111/j.2517-6161.1977.tb01600.x.
  • Feinerer, I., K. Hornik, and D. Meyer. 2008. Text mining infrastructure in R. Journal of Statistical Software 25 (5):1–54. doi:10.18637/jss.v025.i05.
  • Fortunato, S. 2010. Community detection in graphs. Physics Reports 486 (3-5):75–174. doi:10.1016/j.physrep.2009.11.002.
  • Freeman, L. C. 1992. On the sociological concept of” group”: An empirical test of two models. American Journal of Sociology 98 (1):152–66. doi:10.1086/229972.
  • Freeman, L. C. 1993. Finding groups with a simple genetic algorithm. The Journal of Mathematical Sociology 17 (4):227–41. doi:10.1080/0022250X.1993.9990109.
  • Goldenberg, A., A. X. Zheng, S. E. Fienberg, and E. M. Airoldi. 2009. A survey of statistical network models. Foundations and Trends® in Machine Learning 2 (2):129–233. doi:10.1561/2200000005.
  • Holland, P. W., K. B. Laskey, and S. Leinhardt. 1983. Stochastic blockmodels: First steps. Social Networks 5 (2):109–37. doi:10.1016/0378-8733(83)90021-7.
  • Hubert, L., and P. Arabie. 1985. Comparing partitions. Journal of Classification 2 (1):193–218. doi:10.1007/BF01908075.
  • Jaakkola, T. S. 2000. Tutorial on variational approximation methods. In Advanced mean field methods: theory and practice, 129–59. Cambridge, MA: MIT Press.
  • Jaakkola, T. S., and M. I. Jordan. 2000. Bayesian parameter estimation via variational methods. Statistics and Computing 10 (1):25–37. doi:10.1023/A:1008932416310.
  • Jernite, Y., P. Latouche, C. Bouveyron, P. Rivera, L. Jegou, and S. Lamassé. 2014. The random subgraph model for the analysis of an ecclesiastical network in merovingian gaul. Annals of Applied Statistics 8:55–74.
  • Jordan, M. I., Z. Ghahramani, T. S. Jaakkola, and L. K. Saul. 1999. An introduction to variational methods for graphical models. Machine Learning 37 (2):183–233. doi:10.1023/A:1007665907178.
  • Karrer, B., and M. E. J. Newman. 2011. Stochastic blockmodels and community structure in networks. Physical Review E 83 (1):016–107. doi:10.1103/PhysRevE.83.016107.
  • Latouche, P., E. Birmelé, and C. Ambroise. 2011. Overlapping stochastic block models with application to the French political blogosphere. The Annals of Applied Statistics 5 (1):309–36. doi:10.1214/10-AOAS382.
  • Latouche, P., E. Birmelé, and C. Ambroise. 2012. Variational bayesian inference and complexity control for stochastic block models. Statistical Modelling: An International Journal 12 (1):93–115. doi:10.1177/1471082X1001200105.
  • Lei, J. 2016. A goodness-of-fit test for stochastic block models. The Annals of Statistics 44 (1):401–24. doi:10.1214/15-AOS1370.
  • Lewis, D. 1997. Reuters-21578 Text Categorization Collection Distribution 1.0. http://kdd.ics.uci.edu/databases/reuters21578/reuters21578.html.
  • Linton, C. 2003. Finding Social Groups: A Meta-Analysis of the Southern Women Data. In Ronald Breiger, Kathleen Carley and Philippa Pattison, eds. Dynamic Social Network Modeling and Analysis. Washington: The National Academies Press.
  • Mariadassou, M., S. Robin, and C. Vacher. 2010. Uncovering latent structure in valued graphs: A variational approach. The Annals of Applied Statistics 4 (2):715–42. doi:10.1214/10-AOAS361.
  • Matias, C., and V. Miele. 2017. Statistical clustering of temporal networks through a dynamic stochastic block model. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 79 (4):1119–41. doi:10.1111/rssb.12200.
  • McLachlan, G., and T. Krishnan. 2007. The EM algorithm and extensions, 382. Hoboken, NJ: John Wiley and Sons.
  • Nowicki, K., and T. A. B. Snijders. 2001. Estimation and prediction for stochastic blockstructures. Journal of the American Statistical Association 96 (455):1077–87. doi:10.1198/016214501753208735.
  • Osbourn, G. C., and R. F. Martinez. 1995. Empirically defined regions of influence for clustering analyses. Pattern Recognition 28 (11):1793–806. doi:10.1016/0031-3203(95)00032-U.
  • Porter, M. A., J. P. Onnela, and P. J. Mucha. 2009. Communities in networks. Notices of the American Mathematical Society 56:1082–97.
  • Snijders, T. A., and K. Nowicki. 1997. Estimation and prediction for stochastic blockmodels for graphs with latent block structure. Journal of Classification 14 (1):75–100. doi:10.1007/s003579900004.
  • Thomas, A. C., and J. K. Blitzstein. 2011. Valued ties tell fewer lies: Why not to dichotomize network edges with thresholds. arXiv:1101–0788.
  • Xu, K., and A. Hero. III, 2013. Dynamic stochastic blockmodels: Statistical models for time-evolving networks. In Social Computing, Behavioral-Cultural Modeling and Prediction, 201–10. Berlin, Germany: Springer.
  • Yang, T., Y. Chi, S. Zhu, Y. Gong, and R. Jin. 2011. Detecting communities and their evolutions in dynamic social networks: A bayesian approach. Machine Learning 82 (2):157–89. doi:10.1007/s10994-010-5214-7.
  • Zreik, R., P. Latouche, and C. Bouveyron. 2017. The dynamic random subgraph model for the clustering of evolving networks. Computational Statistics 32 (2):501–33. doi:10.1007/s00180-016-0655-5.

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