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

Sandipan Roy

Abstract:

We consider a stochastic blockmodel equipped with node covariate information,
that is helpful in analyzing social network data. The key objective is to obtain max-
imum likelihood estimates of the model parameters. For this task, we devise a fast,
scalable Monte Carlo EM type algorithm based on case-control approximation of the
log-likelihood coupled with a subsampling approach. A key feature of the proposed
algorithm is its parallelizability, by processing portions of the data on several cores,
while leveraging communication of key statistics across the cores during each itera-
tion of the algorithm. The performance of the algorithm is evaluated on synthetic
data sets and compared with competing methods for blockmodel parameter estima-
tion. We also illustrate the model on data from a Facebook derived social network
enhanced with node covariate information