ppsbm

Stochastic block model used for dynamic graphs represented by Poisson processes. To model recurrent interaction events in continuous time, an extension of the stochastic block model is proposed where every individual belongs to a latent group and interactions between two individuals follow a conditional inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. The model is shown to be identifiable and its estimation is based on a semiparametric variational expectation-maximization algorithm. Two versions of the method are developed, using either a nonparametric histogram approach (with an adaptive choice of the partition size) or kernel intensity estimators. The number of latent groups can be selected by an integrated classification likelihood criterion. Y. Baraud and L. Birgé (2009). doi:10.1007/s00440-007-0126-6. C. Biernacki, G. Celeux and G. Govaert (2000). doi:10.1109/34.865189. M. Corneli, P. Latouche and F. Rossi (2016). doi:10.1016/j.neucom.2016.02.031. J.-J. Daudin, F. Picard and S. Robin (2008). doi:10.1007/s11222-007-9046-7. A. P. Dempster, N. M. Laird and D. B. Rubin (1977). . G. Grégoire (1993). . L. Hubert and P. Arabie (1985). doi:10.1007/BF01908075. M. Jordan, Z. Ghahramani, T. Jaakkola and L. Saul (1999). doi:10.1023/A:1007665907178. C. Matias, T. Rebafka and F. Villers (2018). doi:10.1093/biomet/asy016. C. Matias and S. Robin (2014). doi:10.1051/proc/201447004. H. Ramlau-Hansen (1983). doi:10.1214/aos/1176346152. P. Reynaud-Bouret (2006). doi:10.3150/bj/1155735930.