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

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-...

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Bibliographic Details
Published in:Journal of computational and graphical statistics Vol. 28; no. 3; pp. 609 - 619
Main Authors: Roy, Sandipan, Atchadé, Yves, Michailidis, George
Format: Journal Article
Language:English
Published: United States Taylor & Francis 03.07.2019
American Statistical Association, the Institute of Mathematical Statistics, and the Interface Foundation of North America
Taylor & Francis Ltd
Subjects:
Algorithms
Case-control approximation
Computer simulation
Iterative methods
Mathematical models
Maximum likelihood estimates
Monte Carlo EM
Multivariate, Multilevel, and Mixture Modelling
Parallel computation with communication
Parallel processing
Parameter estimation
Social network
Social networks
Subsampling
social network
case-control approximation
Monte-Carlo EM
parallel computation with communication
subsampling
ISSN:1061-8600, 1537-2715
Online Access:Get full text
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Summary: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 datasets 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. Supplemental materials for this article are available online.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2018.1554486