Likelihood Inference for Large Scale Stochastic Blockmodels With Covariates Based on a Divide-and-Conquer Parallelizable Algorithm With Communication

摘要

We consider a stochastic blockmodel equipped with node covariate information,that is useful in analyzing social network data. The objective is to obtainmaximum likelihood estimates of the model parameters. For this task, we devisea fast, scalable Monte Carlo EM type algorithm based on case-controlapproximation of the log-likelihood coupled with a subsampling approach. A keyfeature of the proposed algorithm is its parallelizability, by processingchunks of the data on several cores, while leveraging communication of keystatistics across the cores during every iteration. The performance of thealgorithm is evaluated on synthetic data sets and compared with competingmethods for blockmodel parameter estimation. We also illustrate the model ondata from a Facebook social network enhanced with node covariate information.