Auxiliary Parameter MCMC for Exponential Random Graph Models
- 341 Downloads
Exponential random graph models (ERGMs) are a well-established family of statistical models for analyzing social networks. Computational complexity has so far limited the appeal of ERGMs for the analysis of large social networks. Efficient computational methods are highly desirable in order to extend the empirical scope of ERGMs. In this paper we report results of a research project on the development of snowball sampling methods for ERGMs. We propose an auxiliary parameter Markov chain Monte Carlo (MCMC) algorithm for sampling from the relevant probability distributions. The method is designed to decrease the number of allowed network states without worsening the mixing of the Markov chains, and suggests a new approach for the developments of MCMC samplers for ERGMs. We demonstrate the method on both simulated and actual (empirical) network data and show that it reduces CPU time for parameter estimation by an order of magnitude compared to current MCMC methods.
KeywordsERGMs Parameter inference MCMC Social networks Supercomputing Snowball sampling
This work was funded by PASC project “Snowball sampling and conditional estimation for exponential random graph models for large networks in high performance computing” and was supported by a grant from the Swiss National Supercomputing Centre (CSCS) under project ID c09. This research was also supported by a Victorian Life Sciences Computation Initiative (VLSCI) grant number VR0261 on its Peak Computing Facility at the University of Melbourne, an initiative of the Victorian Government, Australia.
- 24.Wang, P., Robins, G., Pattison, P.: PNet: Program for the Estimation and Simulation of p* Exponential Random Graph Models, User Manual. Department of Psychology, University of Melbourne, Melbourne (2006)Google Scholar
- 29.Barkema, G., Newman, M.: New Monte Carlo algorithms for classical spin systems. arXiv preprint cond-mat/9703179 (1997)Google Scholar
- 32.Pakman, A., Paninski, L.: Auxiliary-variable exact Hamiltonian Monte Carlo samplers for binary distributions. In: Advances in Neural Information Processing Systems, pp. 1–9 (2013)Google Scholar
- 33.Hunter, D.R., Handcock, M.S.: Inference in curved exponential family models for networks. J. Comput. Gr. Stat. 15(3), 565–583 (2006)Google Scholar
- 42.Plummer, M., Best, N., Cowles, K., Vines, K.: CODA: convergence diagnosis and output analysis for MCMC. R News 6(1), 7–11 (2006)Google Scholar