Stochastic Block Transition Models for Dynamic Networks

There has been great interest in recent years on statistical models for dynamic networks. In this paper, I propose a stochastic block transition model (SBTM) for dynamic networks that is inspired by the well-known stochastic block model (SBM) for static networks and previous dynamic extensions of the SBM. Unlike most existing dynamic network models, it does not make a hidden Markov assumption on the edge-level dynamics, allowing the presence or absence of edges to directly influence future edge probabilities while retaining the interpretability of the SBM. I derive an approximate inference procedure for the SBTM and demonstrate that it is significantly better at reproducing durations of edges in real social network data.

[1]  D. Dunson,et al.  Nonparametric Bayes dynamic modelling of relational data , 2013, 1311.4669.

[2]  Mark E. J. Newman,et al.  Stochastic blockmodels and community structure in networks , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  E. Xing,et al.  A state-space mixed membership blockmodel for dynamic network tomography , 2008, 0901.0135.

[4]  Eric A. Wan,et al.  Nonlinear estimation and modeling of noisy time series by dual kalman filtering methods , 2000 .

[5]  Ji Zhu,et al.  Consistency of community detection in networks under degree-corrected stochastic block models , 2011, 1110.3854.

[6]  A. Moore,et al.  Dynamic social network analysis using latent space models , 2005, SKDD.

[7]  Naonori Ueda,et al.  Dynamic Infinite Relational Model for Time-varying Relational Data Analysis , 2010, NIPS.

[8]  Bin Yu,et al.  Spectral clustering and the high-dimensional stochastic blockmodel , 2010, 1007.1684.

[9]  Alfred O. Hero,et al.  Dynamic Stochastic Blockmodels for Time-Evolving Social Networks , 2014, IEEE Journal of Selected Topics in Signal Processing.

[10]  T. Snijders,et al.  Estimation and Prediction for Stochastic Blockstructures , 2001 .

[11]  Purnamrita Sarkar,et al.  A Latent Space Approach to Dynamic Embedding of Co-occurrence Data , 2007, AISTATS.

[12]  Edoardo M. Airoldi,et al.  A Survey of Statistical Network Models , 2009, Found. Trends Mach. Learn..

[13]  J. Norris Appendix: probability and measure , 1997 .

[14]  Zoubin Ghahramani,et al.  Dynamic Probabilistic Models for Latent Feature Propagation in Social Networks , 2013, ICML.

[15]  James R. Foulds,et al.  A Dynamic Relational Infinite Feature Model for Longitudinal Social Networks , 2011, AISTATS.

[16]  Jure Leskovec,et al.  Nonparametric Multi-group Membership Model for Dynamic Networks , 2013, NIPS.

[17]  Peter D. Hoff,et al.  Hierarchical multilinear models for multiway data , 2010, Comput. Stat. Data Anal..

[18]  Krishna P. Gummadi,et al.  On the evolution of user interaction in Facebook , 2009, WOSN '09.

[19]  Yihong Gong,et al.  Detecting communities and their evolutions in dynamic social networks—a Bayesian approach , 2011, Machine Learning.

[20]  Wenjie Fu,et al.  Recovering temporally rewiring networks: a model-based approach , 2007, ICML '07.

[21]  M. Cugmas,et al.  On comparing partitions , 2015 .

[22]  N. H. Lee,et al.  A latent process model for time series of attributed random graphs , 2011 .

[23]  Kathryn B. Laskey,et al.  Stochastic blockmodels: First steps , 1983 .

[24]  Le Song,et al.  Evolving Cluster Mixed-Membership Blockmodel for Time-Evolving Networks , 2011, AISTATS.

[25]  Carey E. Priebe,et al.  A Consistent Adjacency Spectral Embedding for Stochastic Blockmodel Graphs , 2011, 1108.2228.