Reliable Time Prediction in the Markov Stochastic Block Model

We introduce the Markov Stochastic Block Model (MSBM): an extension of the Stochastic Block Model where communities of the nodes are assigned through a Markovian dynamic. We show how MSBMs can be used to detect dependence structure in growing graphs and we provide methods to solve the so-called link prediction and collaborative filtering problems. We make our approaches robust with respect to the outputs of the clustering algorithm and we propose a model selection procedure. Our methods can be applied regardless of the algorithm used to recover communities in the network. In this paper, we use a recent SDP method to infer the hidden communities and we provide theoretical guarantees. In particular, we identify the relevant signal-to-noise ratio (SNR) in our framework and we prove that the misclassification error decays exponentially fast with respect to this SNR.