Fast network community detection with profile-pseudo likelihood methods

The stochastic block model is one of the most studied network models for community detection. 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.