Identifiability and parameter estimation of the overlapped stochastic co-block model

Stochastic block model (SBM) has been extensively studied for undirected network data with community structure, yet its extension to directed network, stochastic co-block model (ScBM), has only been proposed recently. The key difference of the ScBM model is to introduce out- and in-communities to capture different sending and receiving patterns among nodes. In this paper, we further extend the ScBM model so that each node may belong to multiple out- or in-communities. Particularly, we formulate the ScBM model as a generative model, where the unknown community assignment is modeled based on the exclusive or overlapped community. We also establish the corresponding identifiability of the generative ScBM model, and estimate its parameters via an efficient variational EM algorithm. The advantage of the generative ScBM model is demonstrated in a variety of simulated networks and a real political blog network.