Mean-field variational approximate Bayesian inference for latent variable models

Computational Statistics and Data Analysis

Volumn 52, Issue 2, 2007, Pages 790-798

  Consonni, Guido ^a   Marin, Jean Michel ^b  

^a UNIVERSITY OF PAVIA   (Italy)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

Bayesian inference; Bayesian probit model; Gibbs sampling; Latent variable models; Marginal distribution; Mean field variational methods

Indexed keywords

APPROXIMATION ALGORITHMS; BAYESIAN NETWORKS; COMPUTATIONAL LINGUISTICS; MEAN FIELD THEORY; SAMPLING;

BAYESIAN INFERENCE; BAYESIAN PROBIT MODEL; GIBBS SAMPLING; MARGINAL DISTRIBUTION; MEAN-FIELD VARIATIONAL METHODS;

DATA REDUCTION;

EID: 35148829045     PISSN: 01679473     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.csda.2006.10.028     Document Type: Article

References (22)

1. Albert J., and Chib S. Bayesian analysis of binary and polychotomous response data. J. Amer. Statist. Assoc. 88 (1993) 669-679
2. Beal, M., 2003. Variational algorithms for approximate Bayesian inference. Technical Report, Gatsby Computational Neuroscience Unit, Ph.D. Thesis.
3. Beal M., and Ghahramani Z. The variational Bayesian EM algorithm for incomplete data: with application to scoring graphical model structures. Bayesian Statistics vol. 7 (2002), Oxford University Press, Oxford
4. Casella G., and Robert C. Monte Carlo Statistical Methods (1999), Springer, Berlin
5. Cowell R., Dawid A., Lauritzen S., and Spiegelhalter D. Probabilistic Networks and Expert Systems (1999), Springer, Berlin
6. Doucet A., de Freitas N., and Gordon N. Sequential Monte Carlo Methods in Practice (2001), Springer, Berlin
7. Everitt B. An Introduction to Latent Variable Models (1984), Chapman & Hall, London
8. Ghahramani Z., and Beal M. Propagation algorithms for variational Bayesian learning. In: Leen T., Dietterich T., and Tresp V. (Eds). Advances in Neural Information Processing Systems vol. 13 (2001), MIT Press, Cambridge, MA
9. Humphreys K., and Titterington D. Approximate Bayesian inference for simple mixtures. COMPSTAT'2000, Proceedings in Computational Statistics (2000), Springer, Berlin
10. Humphreys K., and Titterington D. Some examples of recursive variational approximations for Bayesian inference. In: Opper M., and Saad D. (Eds). Advances Mean Field Methods: Theory and Practice (2001), MIT Press, Cambridge, MA
11. Jaakkola T. Tutorial on variational approximation methods. In: Opper M., and Saad D. (Eds). Advanced Mean Field Methods: Theory and Practice (2001), MIT Press, Cambridge, MA
12. Jaakkola T., and Jordan M. Bayesian parameter estimation via variational methods. Statist. Comput. 10 (2000) 25-37
13. Jordan M. Graphical models. Statist. Sci. 19 (2004) 140-155
14. Jordan M., Ghahramani Z., Jaakkola T., and Saul K. An introduction to variational methods for graphical models. Mach. Learning 37 2 (1999) 183-233
15. Kass R., and Raftery A. Bayes factor and model uncertainty. J. Amer. Statist. Assoc. 90 (1995) 773-795
16. Lauritzen S. Some modern applications of graphical models. In: Green P., Hjort N., and Richardson S. (Eds). Highly Structured Stochastic Systems (2003), Oxford University Press, Oxford
17. Little R., and Rubin D. Statistical Analysis with Missing Data (1987), Wiley, New York
18. Mclachlan G., and Krishnan T. The EM Algorithm and Extensions (1997), Wiley, New York
19. Ripley B. Stochastic Simulation (1987), Wiley, New York
20. Wang B., and Titterington D. Convergence and asymptotic normality of variational Bayesian approximations for exponential family models with missing values. In: Chickering M., and Halpern J. (Eds). Proceedings of the 20th Conference in Uncertainty in Artificial Intelligence (2004), AUAI Press.
21. Wang B., and Titterington D. Convergence properties of a general algorithm for calculating variational Bayesian estimates for a normal mixture model. Bayesian Anal. 1 3 (2006) 625-650
22. Wiegerinck W. Variational approximations between mean field theory and the junction tree algorithm. In: Boutilier C., and Goldszmidt M. (Eds). Proceedings of the 16th Conference in Uncertainty in Artificial Intelligence (2000), Morgan Kaufmann, Los Altos, CA