Modeling sequences and temporal networks with dynamic community structures

Methods for identification of dynamical patterns in networks suffer from effects of arbitrary time scales that need to be imposed a priori. Here we develop a principled method to identify patterns on dynamics that take place on network systems, as well as on the dynamics that shape the network themselves, without requiring the stipulation of relevant time scales, which instead are determined solely from data. Our approach is based on a variable-order hidden Markov chain model that generalizes the stochastic block model for discrete time-series as well as temporal networks, without requiring the aggregation of events into discrete intervals. We formulate an efficient nonparametric Bayesian framework that can infer the most appropriate Markov order and number of communities, based solely on statistical evidence and without overfitting.