A Fast Inference Algorithm for Stochastic Blockmodel

Stochastic blockmodel is a widely used statistical tool for modeling graphs and networks. Despite its popularity, the development on efficient inference algorithms for this model is surprisingly inadequate. The existing solutions are either too slow to handle large networks, or suffer from convergence issues. In this paper, we propose a fast and principled inference algorithm for stochastic blockmodel. The algorithm is based on the variational Bayesian framework, and deploys the natural conjugate gradient method to accelerate the optimization of the variational bound. Leveraging upon the power of both conjugate and natural gradients, it converges superlinearly and produces high quality solutions in practice. In particular, we apply our algorithm to the community detection task and compare it with the state-of-the-art variational Bayesian algorithms. We show that it can achieve up to two orders of magnitude speedup without significantly compromising the quality of solutions.