  The stochastic block model is one of the most studied network models for
community detection. It is well-known that most algorithms proposed for fitting
the stochastic block model likelihood function cannot scale to large-scale
networks. One prominent work that overcomes this computational challenge is
Amini et al.(2013), which proposed a fast pseudo-likelihood approach for
fitting stochastic block models to large sparse networks. However, this
approach does not have convergence guarantee, and is not well suited for small-
or medium- scale networks. In this article, we propose a novel likelihood based
approach that decouples row and column labels in the likelihood function, which
enables a fast alternating maximization; the new method is computationally
efficient, performs well for both small and large scale networks, and has
provable convergence guarantee. We show that our method provides strongly
consistent estimates of the communities in a stochastic block model. As
demonstrated in simulation studies, the proposed method outperforms the
pseudo-likelihood approach in terms of both estimation accuracy and computation
efficiency, especially for large sparse networks. We further consider
extensions of our proposed method to handle networks with degree heterogeneity
and bipartite properties.
