Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap

Christian S. Schmid, Bruce A. Desmarais, Jr.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an intractable normalizing constant. Simulation methods represent the state-of-the-art approach to approximating the normalizing constant, leading to estimation by Monte Carlo maximum likelihood (MCMLE). MCMLE is accurate when a large sample of networks is used to approximate the normalizing constant. However, MCMLE is computationally expensive, and may be prohibitively so if the size of the network is on the order of 1,000 nodes (i.e., one million potential ties) or greater. When the network is large, one option is maximum pseudolikelihood estimation (MPLE). The standard MPLE is simple and fast, but generally underestimates standard errors. We show that a resampling method - the parametric bootstrap - results in accurate coverage probabilities for confidence intervals. We find that bootstrapped MPLE can be run in 1/5th the time of MCMLE. We study the relative performance of MCMLE and MPLE with simulation studies, and illustrate the two different approaches by applying them to a network of bills introduced in the United State Senate.

Original languageEnglish (US)
Title of host publicationProceedings - 2017 IEEE International Conference on Big Data, Big Data 2017
EditorsZoran Obradovic, Ricardo Baeza-Yates, Jeremy Kepner, Raghunath Nambiar, Chonggang Wang, Masashi Toyoda, Toyotaro Suzumura, Xiaohua Hu, Alfredo Cuzzocrea, Ricardo Baeza-Yates, Jian Tang, Hui Zang, Jian-Yun Nie, Rumi Ghosh
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages116-121
Number of pages6
ISBN (Electronic)9781538627143
DOIs
StatePublished - Jan 12 2018
Event5th IEEE International Conference on Big Data, Big Data 2017 - Boston, United States
Duration: Dec 11 2017Dec 14 2017

Publication series

NameProceedings - 2017 IEEE International Conference on Big Data, Big Data 2017
Volume2018-January

Other

Other5th IEEE International Conference on Big Data, Big Data 2017
CountryUnited States
CityBoston
Period12/11/1712/14/17

Fingerprint

Parametric Bootstrap
Pseudo-likelihood
Graph Model
Random Graphs
Maximum likelihood
Maximum Likelihood
Normalizing Constant
Resampling Methods
Parameter estimation
Coverage Probability
Tie
Standard error
Statistical methods
Simulation Methods
Statistical Analysis
Confidence interval
Parameter Estimation
Graph model
Parametric bootstrap
Random graphs

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Hardware and Architecture
  • Information Systems
  • Information Systems and Management
  • Control and Optimization

Cite this

Schmid, C. S., & Desmarais, Jr., B. A. (2018). Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap. In Z. Obradovic, R. Baeza-Yates, J. Kepner, R. Nambiar, C. Wang, M. Toyoda, T. Suzumura, X. Hu, A. Cuzzocrea, R. Baeza-Yates, J. Tang, H. Zang, J-Y. Nie, ... R. Ghosh (Eds.), Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017 (pp. 116-121). (Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017; Vol. 2018-January). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/BigData.2017.8257919
Schmid, Christian S. ; Desmarais, Jr., Bruce A. / Exponential random graph models with big networks : Maximum pseudolikelihood estimation and the parametric bootstrap. Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017. editor / Zoran Obradovic ; Ricardo Baeza-Yates ; Jeremy Kepner ; Raghunath Nambiar ; Chonggang Wang ; Masashi Toyoda ; Toyotaro Suzumura ; Xiaohua Hu ; Alfredo Cuzzocrea ; Ricardo Baeza-Yates ; Jian Tang ; Hui Zang ; Jian-Yun Nie ; Rumi Ghosh. Institute of Electrical and Electronics Engineers Inc., 2018. pp. 116-121 (Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017).
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abstract = "With the growth of interest in network data across fields, the Exponential Random Graph Model (ERGM) has emerged as the leading approach to the statistical analysis of network data. ERGM parameter estimation requires the approximation of an intractable normalizing constant. Simulation methods represent the state-of-the-art approach to approximating the normalizing constant, leading to estimation by Monte Carlo maximum likelihood (MCMLE). MCMLE is accurate when a large sample of networks is used to approximate the normalizing constant. However, MCMLE is computationally expensive, and may be prohibitively so if the size of the network is on the order of 1,000 nodes (i.e., one million potential ties) or greater. When the network is large, one option is maximum pseudolikelihood estimation (MPLE). The standard MPLE is simple and fast, but generally underestimates standard errors. We show that a resampling method - the parametric bootstrap - results in accurate coverage probabilities for confidence intervals. We find that bootstrapped MPLE can be run in 1/5th the time of MCMLE. We study the relative performance of MCMLE and MPLE with simulation studies, and illustrate the two different approaches by applying them to a network of bills introduced in the United State Senate.",
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Schmid, CS & Desmarais, Jr., BA 2018, Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap. in Z Obradovic, R Baeza-Yates, J Kepner, R Nambiar, C Wang, M Toyoda, T Suzumura, X Hu, A Cuzzocrea, R Baeza-Yates, J Tang, H Zang, J-Y Nie & R Ghosh (eds), Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017. Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017, vol. 2018-January, Institute of Electrical and Electronics Engineers Inc., pp. 116-121, 5th IEEE International Conference on Big Data, Big Data 2017, Boston, United States, 12/11/17. https://doi.org/10.1109/BigData.2017.8257919

Exponential random graph models with big networks : Maximum pseudolikelihood estimation and the parametric bootstrap. / Schmid, Christian S.; Desmarais, Jr., Bruce A.

Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017. ed. / Zoran Obradovic; Ricardo Baeza-Yates; Jeremy Kepner; Raghunath Nambiar; Chonggang Wang; Masashi Toyoda; Toyotaro Suzumura; Xiaohua Hu; Alfredo Cuzzocrea; Ricardo Baeza-Yates; Jian Tang; Hui Zang; Jian-Yun Nie; Rumi Ghosh. Institute of Electrical and Electronics Engineers Inc., 2018. p. 116-121 (Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017; Vol. 2018-January).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Schmid CS, Desmarais, Jr. BA. Exponential random graph models with big networks: Maximum pseudolikelihood estimation and the parametric bootstrap. In Obradovic Z, Baeza-Yates R, Kepner J, Nambiar R, Wang C, Toyoda M, Suzumura T, Hu X, Cuzzocrea A, Baeza-Yates R, Tang J, Zang H, Nie J-Y, Ghosh R, editors, Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017. Institute of Electrical and Electronics Engineers Inc. 2018. p. 116-121. (Proceedings - 2017 IEEE International Conference on Big Data, Big Data 2017). https://doi.org/10.1109/BigData.2017.8257919