Inadequacy of interval estimates corresponding to variational Bayesian approximations

AISTATS 2005 - Proceedings of the 10th International Workshop on Artificial Intelligence and Statistics

Volumn , Issue , 2005, Pages 373-380

  Wang, Bo ^a   Titterington, D M ^a  

^a UNIVERSITY OF GLASGOW   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANCE MATRICES; FISHER INFORMATION MATRICES; INTERVAL ESTIMATE; MAXIMUM LIKELIHOOD ESTIMATOR; MIXTURE MODEL; VARIATIONAL BAYES APPROXIMATIONS; VARIATIONAL BAYESIAN;

ARTIFICIAL INTELLIGENCE; FISHER INFORMATION MATRIX; MAXIMUM LIKELIHOOD ESTIMATION;

COVARIANCE MATRIX;

EID: 62149086004     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (18)

1. Attias, H. (1999). Inferring parameters and structure of latent variable models by variational Bayes. In Prade, H. and Laskey, K., editors, Proc. 15th Conference on Uncertainty in Artificial Intelligence, pages 21-30, Stockholm, Sweden. Morgan Kaufmann Publishers.
2. Attias, H. (2000). A variational Bayesian framework for graphical models. In Solla, S., Leen, T., and Muller, K.-R., editors, Advances in Neural Information Processing Systems 12, pages 209-215. MIT Press, Cambridge, MA.
3. Beal, M. J. (2003). Variational Algorithms for Approximate Bayesian Inference. PhD thesis, University College London.
4. Chen, C.-F. (1985). On asymptotic normality of limiting density functions with Bayesian implications. J. R. Statist. Soc. B, 47:540-546.
5. Consonni, G. and Marin, J.-M. (2004). A note on variational approximate bayesian inference for latent variable models. Preprint.
6. Ghahramani, Z. and Beal, M. J. (2000). Variational inference for Bayesian mixtures of factor analysers. In Solla, S., Leen, T., and Muller, K.-R., editors, Advances in Neural Information Processing Systems 12, pages 449-455. MIT Press, Cambridge, MA.
7. Ghahramani, Z. and Beal, M. J. (2001). Propagation algorithms for variational Bayesian learning. In Leen, T., Dietterich, T., and Tresp, V., editors, Advances in Neural Information Processing Systems 13, pages 507-513. MIT Press, Cambridge, MA.
8. Ghosal, S., Ghosh, J. K., and Samanta, T. (1995). On convergence of posterior distributions. The Annals of Statistics, 23(6):2145-2152.
9. Humphreys, K. and Titterington, D. M. (2000). Approximate Bayesian inference for simple mixtures. In Bethlehem, J. G. and van der Heijden, P. G. M., editors, COMPSTAT2000, pages 331-336. Physica-Verlag, Heidelberg.
10. Jordan, M. I. (2004). Graphical models. Statistical Science, 19(1):140-155.
11. MacKay, D. J. C. (1997). Ensemble learning for hidden Markov models. Technical report, Cavendish Laboratory, University of Cambridge.
12. Penny, W. D. and Roberts, S. J. (2000). Variational Bayes for 1-dimensional mixture models. Technical Report PARG-2000-01, Oxford University.
13. Peters, B. C. and Walker, H. F. (1978). An iterative procedure for obtaining maximum-likelihood estimates of the parameters for a mixture of normal distributions. SIAM J. Appl. Math., 35:362-378.
14. Redner, R. A. and Walker, H. F. (1984). Mixture densities, maximum likelihood and the EM algorithm. SIAM Review, 26:195-239.
15. Walker, A. M. (1969). On the asymptotic behaviour of posterior distributions. J. R. Statist. Soc. B, 31:80-88.
16. Wang, B. and Titterington, D. M. (2003). Local convergence of variational Bayes estimators for mixing coefficients. Technical Report 03-4, University of Glasgow. http://www.stats.gla.ac.uk/Research/-TechRep2003/03-4.pdf.
17. Wang, B. and Titterington, D. M. (2004a). Convergence and asymptotic normality of variational Bayesian approximations for exponential family models with missing values. In Chickering, M. and Halpern, J., editors, Proceedings of the twentieth conference on Uncertainty in Artificial Intelligence, pages 577-584, Banff, Canada. AUAI Press.
18. Wang, B. and Titterington, D. M. (2004b). Convergence properties of a general algorithm for calculating variational Bayesian estimates for a normal mixture model. Technical Report 04-3, University of Glasgow. http://www.stats.gla.ac.uk/Research/-TechRep2004/043.pdf.