Multi-level stochastic block models for multiplex networks

Multiplex arises when the network for the same set of nodes is repetitively observed on different layers that can represent, for instance, different statistical units or different criteria to connect the nodes. A multi-level Stochastic Blockmodel for multiplexes is introduced to provide a joint clustering of layers and nodes. This is achieved by considering two different sets of discrete latent variables. A former set allows us identifying groups of layers sharing similar connectivity patterns. A latter set of discrete latent variables, nested within the former, allows us identifying groups of nodes sharing similar relational features. A variational Expectation-Maximization algorithm is derived for estimation purposes.