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Title: Estimating the number of clusters in a stochastic block model for temporal networks Authors:  Riccardo Rastelli - University College Dublin (Ireland) [presenting]
Pierre Latouche - Sorbonne university (France)
Nial Friel - University College Dublin (Ireland)
Abstract: The latent Stochastic Block Model is a flexible and widely used statistical model for networks that can be generalized to a dynamic context, where interactions are observed at a number of different time frames. This model hypothesizes a latent clustering structure on the nodes of the network, and for this reason it shares many similarities with mixture models. In this context, techniques such as the Expectation-Maximization algorithm usually require a variational approximation on the posterior distribution to be used. We will show that, under general assumptions, it is possible to analytically integrate out most of the model parameters of a dynamic Stochastic Block Model. This leads to an exact formula for a model-based criterion: the Integrated Completed Likelihood (ICL). In this formulation the ICL depends on the model parameters only through the nodes' allocations. We will illustrate a greedy discrete optimization tool that can maximize the ICL, hence returning both the optimal clustering and the optimal model in one algorithmic framework. One important advantage of this approach is that it does not rely on any approximation of the posterior distribution or of the model-based criterion. The algorithm proposed over-performs other existing procedures both in terms of model-choice accuracy and computational complexity. We will show applications of the methodology to both simulated networks and to a real dataset of bike hires in London.