Bayesian Parameter Estimation for Latent Markov Random Fields and Social Networks

By Richard Geoffrey Everitt. 2012

103 citations recorded by the source corpus.

Undirected graphical models are widely used in statistics, physics, and machine vision. However, Bayesian parameter estimation for undirected models is extremely challenging, since evaluation of the posterior typically involves the calculation of an intractable normalizing constant. This problem has received much attention, but very little of this has focused on the important practical case where the data consist of noisy or incomplete observations of the underlying hidden structure. This article specifically addresses this problem, comparing two alternate methodologies. In the first of these approaches, particle Markov chain Monte Carlo (Andrieu, Doucet, and Holenstein) is used to efficiently explore the parameter space, combined with the exchange algorithm (Murray, Ghahramani, and MacKay) for avoiding the calculation of the intractable normalizing constant (a proof showing that this combination targets the correct distribution is given in Appendix A available in the online supplementary materials). This approach is compared with approximate Bayesian computation (Pritchard et al.). Applications to estimating the parameters of Ising models and exponential random graphs from noisy data are presented. Each algorithm used in the article targets an approximation to the true posterior due to the use of Markov chain Monte Carlo method (MCMC) to simulate from the latent graphical model, in lieu of being able to do this exactly, in general. Appendix B (online supplementary materials) also describes the nature of the resulting approximation. Supplementary materials for this article are available online.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Control functionals for Monte Carlo integration (2014, methodology): “Markov random fields (Everitt, 2012) and random network models (Friel et al.”
Exploiting Multi-Core Architectures for Reduced-Variance Estimation with Intractable Likelihoods (2014, background): “6: end for out, and in this case Everitt (2012) has provided convergence results for the case where one uses the ﬁnal draw from a Gibbs sampler targeting the likelihood as an approximate realisation.”
On nonnegative unbiased estimators (2013, background): “In other settings, the likelihood cannot be evaluated because it involves an intractable quantity, as “doubly intractable” posterior distributions commonly found in spatial statistics and graphical models (Møller et al., 2006; Everitt, 2012).”
Interacting Particle Markov Chain Monte Carlo (2016, methodology): “An additional advantage of the iPMCMC method is that it is suitable for distributed and multi-core architectures.”