Likelihood Inference for Large Scale Stochastic Blockmodels With Covariates Based on a Divide-and-Conquer Parallelizable Algorithm With Communication |
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Authors: | Sandipan Roy Yves Atchadé George Michailidis |
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Affiliation: | 1. Department of Statistical Science, University College London, London, UK;2. sandipan@umich.edu;4. Department of Statistics, University of Michigan, Ann Arbor, MI;5. Department of Statistics &6. Informatics Institute, University of Florida, Gainesville, FL |
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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 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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Keywords: | Case-control approximation Monte Carlo EM Parallel computation with communication Social network Subsampling |
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