Convergence properties of a general algorithm for calculating variational Bayesian estimates for a normal mixture model

By Bo Wang, D. M. Titterington. 2006

146 citations recorded by the source corpus.

In this paper we propose a generalised iterative algorithm for calcu- lating variational Bayesian estimates for a normal mixture model and investigate its convergence properties. It is shown theoretically that the variational Bayesian estimator converges locally to the maximum likelihood estimator at the rate of O(1=n) in the large sample limit.

Subfields: Artificial Intelligence, Statistics and Probability

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Citations in the corpus

Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations (2009, unknown): “First, even though VB methods seem often to approximate well the posterior mode (Wang and Titterington, 2006), the posterior variance can be (sometimes severely) underestimated; see Bishop (2006), chapter 10, and Wang and Titterington (2005).”
Convergence and Asymptotic Normality of Variational Bayesian Approximations for Expon (2004, background): “On the other hand we showed in [15] that variational Bayes estimators for certain mixture models are asymptotically efficient for large sample sizes.”
A variational Bayes approach to variable selection (2017, background): “Such criticism can be made on empirical, e.g., Wand et al. (2011); Carbonetto and Stephens (2011), or theoretical grounds, e.g., Wang and Titterington (2006); Rue et al. (2009).”
Variational approximations in Bayesian model selection for finite mixture distributions (2007, methodology): “For example, in Wang and Titterington (2006) they demonstrated the consistency of the variational posterior modes of the parameters in mixtures of multivariate Gaussian distributions.”
Inadequacy of interval estimates corresponding to variational Bayesian approximations (2005, background): “Some initial investigations have been implemented by the authors in Wang and Titterington (2003) and Wang and Titterington (2004b).”
Theory of Gaussian variational approximation for a Poisson mixed model (2011, background): “Almost all of the variational approximation theory of which we are aware treats Bayesian inferential settings (e.g. Humphreys & Titterington, 2000; Wang & Titterington, 2006).”
Explaining Variational Approximations (2010, background): “…(2007) and McGrory, Titterington, Reeves & Pettitt (2009) on new variational approximation methodology for particular applications, and Hall, Humphreys & Titterington (2002) and Wang & Titterington (2006) on the statistical properties of estimators obtained via variational approximation.”