Abstract
Various kinds of data such as social media can be represented as a network or graph. Latent variable models using Bayesian statistical inference are powerful tools to represent such networks. One such latent variable network model is a Mixed Membership Stochastic Blockmodel (MMSB), which can discover overlapping communities in a network and has high predictive power. Previous inference methods estimate the latent variables and unknown parameters of the MMSB on the basis of the whole observed network. Therefore, dynamic changes in network structure over time are hard to track. Thus, we first present an incremental Gibbs sampler based on node activities that focuses only on observations within a fixed term length for online sequential estimation of the MMSB. We further present a particle filter based on node activities with various term lengths. For instance, in an e-mail communication network, each particle only considers e-mail accounts that sent or received a message within a specific term length, where the length may be different from those of other particles. We show through experiments with two link prediction datasets that our proposed methods achieve both high prediction performance and computational efficiency.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
In this paper, we assume a directed graph for representing the network structure, but the network structure can also be easily applied to an undirected graph.
- 2.
In Sect. 3.1, we used an indicator vector \(\mathbf {z}_{p \rightarrow q}\) where a specific component is one, corresponding to the group indicated by \(z_{p \rightarrow q}\), and all the others are zero, for convenience.
References
Airoldi, E.M., Blei, D.M., Fienberg, S.E., Xing, E.P.: Mixed membership stochastic blockmodels. J. Mach. Learn. Res. 9, 1981–2014 (2008)
Ball, B., Karrer, B., Newman, M.E.J.: Efficient and principled method for detecting communities in networks. Phys. Rev. E 84(3), 036103 (2011)
Blei, D.M., Ng, A.Y., Jordan, M.I.: Latent Dirichlet allocation. J. Mach. Learn. Res. 3, 993–1022 (2003)
Canini, K.R., Shi, L., Griffiths, T.L.: Online inference of topics with latent Dirichlet allocation. In: Proceedings of the 12th International Conference on Artificial Intelligence and Statistics, Clearwater Beach, Florida, USA, pp. 65–72 (2009)
Doucet, A., de Freitas, N., Gordon, N. (eds.): Sequential Monte Carlo Methods in Practice. Springer, New York (2001). https://doi.org/10.1007/978-1-4757-3437-9
Ghahramani, Z., Griffiths, T.L.: Infinite latent feature models and the Indian buffet process. In: Advances in Neural Information Processing Systems, vol. 18 (2006)
Goldenberg, A., Zheng, A.X., Fienberg, S.E., Airoldi, E.M.: A survey of statistical network models. Found. Trends Mach. Learn. 2(2), 129–233 (2010)
Gopalan, P.K., Gerrish, S., Freedman, M., Blei, D.M., Mimno, D.M.: Scalable inference of overlapping communities. In: Advances in Neural Information Processing Systems, vol. 25 (2012)
Griffiths, T.L., Steyvers, M.: Finding scientific topics. Proc. Natl. Acad. Sci. U. S. A. 101, 5228–5235 (2004)
Hofmann, T.: Probabilistic latent semantic indexing. In: Proceedings of the 22nd Annual International ACM SIGIR Conference on Research and Development in Information Retrieval, Berkeley, California, USA, pp. 50–57 (1999)
Iwata, T., Yamada, T., Sakurai, Y., Ueda, N.: Sequential modeling of topic dynamics with multiple timescales. ACM Trans. Knowl. Discov. Data 5(4) (2012)
Karrer, B., Newman, M.E.J.: Stochastic blockmodels and community structure in networks. Phys. Rev. E 83, 016107 (2011)
Kemp, C., Tenenbaum, J.B., Griffiths, T.L., Yamada, T., Ueda, N.: Learning systems of concepts with an infinite relational model. In: Proceedings of the 21st National Conference on Artificial Intelligence, Boston, Massachusetts, USA, vol. 1, pp. 381–388 (2006)
Klimt, B., Yang, Y.: Introducing the Enron corpus. In: First Conference on Email and Anti-Spam CEAS, Mountain View, California, USA (2004)
Kobayashi, T., Eguchi, K.: Online inference of mixed membership stochastic blockmodels for network data streams. IEICE Trans. Inf. Syst. E97-D(4), 752–761 (2014)
Miller, K.T., Jordan, M.I., Griffiths, T.L.: Nonparametric latent feature models for link prediction. In: Advances in Neural Information Processing Systems, vol. 22, pp. 1276–1284 (2009)
Nowicki, K., Snijders, T.A.B.: Estimation and prediction for stochastic blockstructures. J. Am. Stat. Assoc. 96(455), 1077–1087 (2001)
Opsahl, T., Panzarasa, P.: Clustering in weighted networks. Soc. Netw. 31(2), 155–163 (2009)
Snijders, T.A.B., Nowicki, K.: Estimation and prediction for stochastic blockmodels for graphs with latent block structure. J. Classif. 14, 75–100 (1997)
Acknowledgments
This work was supported in part by the Grant-in-Aid for Scientific Research (#15H02703) from JSPS, Japan.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Switzerland AG
About this paper
Cite this paper
Sakamoto, S., Eguchi, K. (2019). Sequential Monte Carlo Inference Based on Activities for Overlapping Community Models. In: Atzmueller, M., Chin, A., Lemmerich, F., Trattner, C. (eds) Behavioral Analytics in Social and Ubiquitous Environments. MUSE MSM MSM 2015 2015 2016. Lecture Notes in Computer Science(), vol 11406. Springer, Cham. https://doi.org/10.1007/978-3-030-34407-8_5
Download citation
DOI: https://doi.org/10.1007/978-3-030-34407-8_5
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-33906-7
Online ISBN: 978-3-030-34407-8
eBook Packages: Computer ScienceComputer Science (R0)