Statistical analysis of graphs with abrupt changes

Abstract

Graphs are powerful mathematical tools to express relationships between any kind of items in very diverse disciplines. In this work, we worked on stochastic block models and multiple change-point detection problem for graph time series, where number of change points is unknown. Stochastic block models is a branch of clustering algorithms for relational data. We studied bayesian approaches as expectationmaximization (EM), variational expectation-maximization, Monte Carlo methods as Gibbs sampling for analysis of stochastic block models. For time series analysis, we have studied Hidden Markov Models, applied well-known forward-backward algorithm to multiple change point analysis on network series. We have proposed an approximate inference algorithm that combines Monte Carlo approaches and hidden Markov models (forward ltering-backward sampling). In our model, we calculate the forward messages completely, sample a change point from those, calculate the backward message for the sampled changed point, update with the forward message and sample a change point for the previous time step. It continues in this way to the rst time step, named backward-sampling. By this way, we have simpli ed the calculation cost. In addition, it is a motivation to use Monte Carlo methodologies in time series analysis where we can not take integrals easily in order to do exact inference. On experiments we have done on syntheic data, we have seen that our proposed approximate inference algorithm gives results in accordance with exact inference methodology, in detecting multiple change points and category assignments.