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

TL;DR

This paper introduces a scalable, parallelizable Monte Carlo EM algorithm for likelihood inference in large-scale stochastic blockmodels with covariates, improving efficiency and accuracy in social network analysis.

Contribution

It presents a novel divide-and-conquer algorithm that enables fast, parallelized maximum likelihood estimation for large stochastic blockmodels with covariates, incorporating communication between cores.

Findings

Algorithm performs well on synthetic data.

Outperforms existing methods in speed and accuracy.

Successfully applied to real Facebook social network data.

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 maximum 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 iteration of the algorithm. The performance of the algorithm is evaluated on synthetic data sets and compared with competing methods for blockmodel parameter estimation. We also illustrate the model on data from a Facebook derived social network enhanced with node covariate information.