Bayesian Variational Inference for Exponential Random Graph Models
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs,...
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| Vydané v: | Journal of computational and graphical statistics Ročník 29; číslo 4; s. 910 - 928 |
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| Jazyk: | English |
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Alexandria
Taylor & Francis
01.10.2020
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| Abstract | Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using, for instance, a "tie no tie" sampler. In this article, we develop a variety of variational methods for Gaussian approximation of the posterior density and model selection. These include nonconjugate variational message passing based on an adjusted pseudolikelihood and stochastic variational inference. To overcome the computational hurdle of drawing a network from the likelihood at each iteration, we propose stochastic gradient ascent with biased but consistent gradient estimates computed using adaptive self-normalized importance sampling. These methods provide attractive fast alternatives to MCMC for posterior approximation. We illustrate the variational methods using real networks and compare their accuracy with results obtained via MCMC and Laplace approximation.
Supplementary materials
for this article are available online. |
|---|---|
| AbstractList | Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using, for instance, a "tie no tie" sampler. In this article, we develop a variety of variational methods for Gaussian approximation of the posterior density and model selection. These include nonconjugate variational message passing based on an adjusted pseudolikelihood and stochastic variational inference. To overcome the computational hurdle of drawing a network from the likelihood at each iteration, we propose stochastic gradient ascent with biased but consistent gradient estimates computed using adaptive self-normalized importance sampling. These methods provide attractive fast alternatives to MCMC for posterior approximation. We illustrate the variational methods using real networks and compare their accuracy with results obtained via MCMC and Laplace approximation.
Supplementary materials
for this article are available online. Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging “doubly intractable” problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC) methods which yield Bayesian inference for ERGMs, such as the exchange algorithm, are asymptotically exact but computationally intensive, as a network has to be drawn from the likelihood at every step using, for instance, a “tie no tie” sampler. In this article, we develop a variety of variational methods for Gaussian approximation of the posterior density and model selection. These include nonconjugate variational message passing based on an adjusted pseudolikelihood and stochastic variational inference. To overcome the computational hurdle of drawing a network from the likelihood at each iteration, we propose stochastic gradient ascent with biased but consistent gradient estimates computed using adaptive self-normalized importance sampling. These methods provide attractive fast alternatives to MCMC for posterior approximation. We illustrate the variational methods using real networks and compare their accuracy with results obtained via MCMC and Laplace approximation. Supplementary materials for this article are available online. |
| Author | Friel, Nial Tan, Linda S. L. |
| Author_xml | – sequence: 1 givenname: Linda S. L. surname: Tan fullname: Tan, Linda S. L. email: statsll@nus.edu.sg organization: Department of Statistics and Applied Probability, National University of Singapore – sequence: 2 givenname: Nial surname: Friel fullname: Friel, Nial organization: School of Mathematics and Statistics, University College Dublin |
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| SubjectTerms | Adaptive sampling Adaptive self-normalized importance sampling Adjusted pseudolikelihood Algorithms Approximation Ascent Bayesian analysis Density Exponential random graph model Importance sampling Importance weighted lower bound Iterative methods Markov chains Mathematical analysis Message passing Monte Carlo simulation Nonconjugate variational message passing Normalizing (statistics) Statistical inference Stochastic variational inference Variational methods |
| Title | Bayesian Variational Inference for Exponential Random Graph Models |
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