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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Veröffentlicht in:Journal of computational and graphical statistics Jg. 29; H. 4; S. 910 - 928
Hauptverfasser: Tan, Linda S. L., Friel, Nial
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Alexandria Taylor & Francis 01.10.2020
Taylor & Francis Ltd
Schlagworte:
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
ISSN:1061-8600, 1537-2715
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Zusammenfassung: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.
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ISSN:1061-8600
1537-2715
DOI:10.1080/10618600.2020.1740714