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

Sandipan Roy, Yves Atchadé, George Michailidis

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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.

Original languageEnglish
Pages (from-to)609-619
Number of pages12
JournalJournal of Computational and Graphical Statistics
Volume28
Issue number3
Early online date27 Feb 2019
DOIs
Publication statusPublished - 10 Jul 2019

Keywords

  • Case-control approximation
  • Monte Carlo EM
  • Parallel computation with communication
  • Social network
  • Subsampling

ASJC Scopus subject areas

  • Statistics and Probability
  • Discrete Mathematics and Combinatorics
  • Statistics, Probability and Uncertainty

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