Mixed membership blockmodels for dynamic networks with feedback

Abstract

Real-world networks are inherently complex dynamical systems, where both node attributes and network topology change in time. These changes often affect each other, providing complex feedback mechanisms between node and link dynamics. Here we propose a dynamic mixed membership model of networks that explicitly take into account such feedback. In the proposed model, the probability of observing a link between two nodes depends on their current group membership vectors, while those membership vectors themselves evolve in the presence of a link between the nodes. Thus, the network is shaped by the interaction of stochastic processes describing the nodes, while the processes themselves are influenced by the changing network structure. We derive an efficient variational procedure for inference, and validate the model using both synthetic and real-world data.