Bayesian variational inference for exponential random graph models

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Title: Bayesian variational inference for exponential random graph models
Authors: Tan, Linda S. L.Friel, Nial
Permanent link: http://hdl.handle.net/10197/12008
Date: 15-Apr-2020
Online since: 2021-03-04T16:51:03Z
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.
Funding Details: Science Foundation Ireland
Funding Details: Insight Research Centre
Type of material: Journal Article
Publisher: Taylor & Francis
Journal: Journal of Computational and Graphical Statistics
Volume: 29
Issue: 4
Start page: 910
End page: 928
Keywords: Adjusted pseudolikelihoodAdaptive self-normalozed importance samplingExpontential random graph modelNonconjugate variational message passingStochastic variational inference
DOI: 10.1080/10618600.2020.1740714
Language: en
Status of Item: Peer reviewed
This item is made available under a Creative Commons License: https://creativecommons.org/licenses/by-nc-nd/3.0/ie/
Appears in Collections:Mathematics and Statistics Research Collection
Insight Research Collection

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