1,449
Views
15
CrossRef citations to date
0
Altmetric
Theory and Methods

Variational Inference for Stochastic Block Models From Sampled Data

, &
Pages 455-466 | Received 25 Aug 2017, Accepted 18 Dec 2018, Published online: 11 Apr 2019

References

  • Aicher, C., Jacobs, A. Z., and Clauset, A. (2014), “Learning Latent Block Structure in Weighted Networks,” Journal of Complex Networks, 3, 221–248. DOI: 10.1093/comnet/cnu026.
  • Airoldi, E. M., Blei, D. M., Fienberg, S. E., and Xing, E. P. (2008), “Mixed Membership Stochastic Blockmodels,” Journal of Machine Learning Research, 9, 1981–2014.
  • Ashburner, M., Ball, C. A., Blake, J. A., Botstein, D., Butler, H., Cherry, J. M., Davis, A. P., Dolinski, K., Dwight, S. S., Eppig, J. T., and Harris, M. A. (2000), “Gene Ontology: Tool for the Unification of Biology,” Nature Genetics, 25, 25. DOI: 10.1038/75556.
  • Balachandran, P., Kolaczyk, E. D., and Viles, W. D. (2017), “On the Propagation of Low-Rate Measurement Error to Subgraph Counts in Large Networks,” Journal of Machine Learning Research, 18, 1–33.
  • Barbillon, P., Donnet, S., Lazega, E., and Bar-Hen, A. (2015), “Stochastic Block Models for Multiplex Networks: An Application to Networks of Researchers,” Journal of the Royal Statistical Society, Series A, 180, 295–314. DOI: 10.1111/rssa.12193.
  • Bickel, P., Choi, D., Chang, X., and Zhang, H. (2013), “Asymptotic Normality of Maximum Likelihood and Its Variational Approximation for Stochastic Blockmodels,” The Annals of Statistics, 41, 1922–1943. DOI: 10.1214/13-AOS1124.
  • Biernacki, C., Celeux, G., and Govaert, G. (2000), “Assessing a Mixture Model for Clustering With the Integrated Completed Likelihood,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 719–725. DOI: 10.1109/34.865189.
  • Celisse, A., Daudin, J.-J., and Pierre, L. (2012), “Consistency of Maximum-Likelihood and Variational Estimators in the Stochastic Block Model,” Electronic Journal of Statistics, 6, 1847–1899. DOI: 10.1214/12-EJS729.
  • Chatterjee, S. (2015), “Matrix Estimation by Universal Singular Value Thresholding,” The Annals of Statistics, 43, 177–214. DOI: 10.1214/14-AOS1272.
  • Daudin, J.-J., Picard, F., and Robin, S. (2008), “A Mixture Model for Random Graphs,” Statistics and Computing, 18, 173–183. DOI: 10.1007/s11222-007-9046-7.
  • Davenport, M. A., Plan, Y., van den Berg, E., and Wootters, M. (2014), “1-Bit Matrix Completion,” Information and Inference, 3, 189–223. DOI: 10.1093/imaiai/iau006.
  • Frank, O., and Harary, F. (1982), “Cluster Inference by Using Transitivity Indices in Empirical Graphs,” Journal of the American Statistical Association, 77, 835–840. DOI: 10.1080/01621459.1982.10477895.
  • Goldenberg, A., Zheng, A. X., Fienberg, S. E., and Airoldi, E. M. (2010), “A Survey of Statistical Network Models,” Foundations and Trends® in Machine Learning, 2, 129–233. DOI: 10.1561/2200000005.
  • Handcock, M. S., and Gile, K. J. (2010), “Modeling Social Networks From Sampled Data,” The Annals of Applied Statistics, 4, 5–25. DOI: 10.1214/08-AOAS221.
  • Holland, P. W., Laskey, K. B., and Leinhardt, S. (1983), “Stochastic Blockmodels: First Steps,” Social Networks, 5, 109–137. DOI: 10.1016/0378-8733(83)90021-7.
  • Jordan, M. I., Ghahramani, Z., Jaakkola, T. S., and Saul, L. K. (1998), “An Introduction to Variational Methods for Graphical Models,” in Learning in Graphical Models, Dordrecht: Springer, pp. 105–161.
  • Karrer, B., and Newman, M. E. J. (2011), “Stochastic Blockmodels and Community Structure in Networks,” Physical Review E, 83, 016107. DOI: 10.1103/PhysRevE.83.016107.
  • Kolaczyk, E. D. (2009), Statistical Analysis of Network Data, Methods and Models, New York: Springer.
  • Labeyrie, V., Deu, M., Barnaud, A., Calatayud, C., Buiron, M., Wambugu, P., Manel, S., Glaszmann, J.-C., and Leclerc, C. (2014), “Influence of Ethnolinguistic Diversity on the Sorghum Genetic Patterns in Subsistence Farming Systems in Eastern Kenya,” PLoS One, 9, e92178. DOI: 10.1371/journal.pone.0092178.
  • Labeyrie, V., Thomas, M., Muthamia, Z. K., and Leclerc, C. (2016), “Seed Exchange Networks, Ethnicity, and Sorghum Diversity,” Proceedings of the National Academy of Sciences of the United States of America, 113, 98–103. DOI: 10.1073/pnas.1513238112.
  • Latouche, P., Birmelé, É., and Ambroise, C. (2011), “Overlapping Stochastic Block Models With Application to the French Political Blogosphere,” The Annals of Applied Statistics, 5, 309–336. DOI: 10.1214/10-AOAS382.
  • Latouche, P., Birmelé, É., and Ambroise, C. (2012), “Variational Bayesian Inference and Complexity Control for Stochastic Block Models,” Statistical Modelling, 12, 93–115.
  • Latouche, P., Robin, S., and Ouadah, S. (2017), “Goodness of Fit of Logistic Models for Random Graphs,” Technical Report, arXiv no. 1508.00286.
  • Little, R. J., and Rubin, D. B. (2014), Statistical Analysis With Missing Data, Hoboken, NJ: Wiley.
  • Mariadassou, M., Robin, S., and Vacher, C. (2010), “Uncovering Latent Structure in Valued Graphs: A Variational Approach,” The Annals of Applied Statistics, 4, 715–742. DOI: 10.1214/10-AOAS361.
  • Matias, C., and Miele, V. (2016), “Statistical Clustering of Temporal Networks Through a Dynamic Stochastic Block Model,” Journal of the Royal Statistical Society, Series B, 79, 1119–1141. DOI: 10.1111/rssb.12200.
  • Matias, C., and Robin, S. (2014), “Modeling Heterogeneity in Random Graphs Through Latent Space Models: A Selective Review,” ESAIM: Proceedings and Surveys, 47, 55–74. DOI: 10.1051/proc/201447004.
  • Molenberghs, G., Beunckens, C., Sotto, C., and Kenward, G. M. (2008), “Every Missing Not at Random Model Has Got a Missing at Random Counterpart With Equal Fit,” Journal of the Royal Statistical Society, Series B, 70, 371–388. DOI: 10.1111/j.1467-9868.2007.00640.x.
  • Nowicki, K., and Snijders, T. A. B. (2001), “Estimation and Prediction for Stochastic Blockstructures,” Journal of the American Statistical Association, 96, 1077–1087. DOI: 10.1198/016214501753208735.
  • Priebe, C. E., Sussman, D. L., Tang, M., and Vogelstein, J. T. (2015), “Statistical Inference on Errorfully Observed Graphs,” Journal of Computational and Graphical Statistics, 24, 930–953. DOI: 10.1080/10618600.2014.951049.
  • Rand, W. M. (1971), “Objective Criteria for the Evaluation of Clustering Methods,” Journal of the American Statistical Association, 66, 846–850. DOI: 10.1080/01621459.1971.10482356.
  • Rubin, D. B. (1976), “Inference and Missing Data,” Biometrika, 63, 581–592. DOI: 10.1093/biomet/63.3.581.
  • Snijders, T. A. (2011), “Statistical Models for Social Networks,” Annual Review of Sociology, 37, 131–153. DOI: 10.1146/annurev.soc.012809.102709.
  • Snijders, T. A., and Nowicki, K. (1997), “Estimation and Prediction for Stochastic Blockmodels for Graphs With Latent Block Structure,” Journal of Classification, 14, 75–100. DOI: 10.1007/s003579900004.
  • Szklarczyk, D., Franceschini, A., Wyder, S., Forslund, K., Heller, D., Huerta-Cepas, J., Simonovic, M., Roth, A., Santos, A., Tsafou, K. P., and Kuhn, M. (2015), “String v10: Protein–Protein Interaction Networks, Integrated Over the Tree of Life,” Nucleic Acids Research, 43, D447–D452. DOI: 10.1093/nar/gku1003.
  • Thompson, S. K., and Frank, O. (2000), “Model-Based Estimation With Link-Tracing Sampling Designs,” Survey Methodology, 26, 87–98.
  • Thompson, S. K., and Seber, G. (1996), Adaptive Sampling, New York: Wiley.
  • Vinayak, R. K., Oymak, S., and Hassibi, B. (2014), “Graph Clustering With Missing Data: Convex Algorithms and Analysis,” in Advances in Neural Information Processing.
  • Vincent, K., and Thompson, S. (2015), “Estimating the Size and Distribution of Networked Populations With Snowball Sampling,” Technical Report, arXiv no. 1402.4372v2.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.