Bayesian parameter estimation via variational methods

Statistics and Computing

Volumn 10, Issue 1, 2000, Pages 25-37

  Jaakkola, Tommi S ^a   Jordan, Michael I ^b  

^a Massachusetts Inst of Technology ^*  (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Bayesian estimation; Belief networks; Graphical models; Incomplete data; Logistic regression; Variational methods

Indexed keywords

EID: 0042685161     PISSN: 09603174     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1008932416310     Document Type: Article

References (20)

1. Bernardo J. and Smith A. 1994. Bayesian Theory. New York, Wiley.
2. Everitt B. 1984. An Introduction to Latent Variable Models. Cambridge University Press.
3. Gelman A. 1995. Bayesian Data Analysis. Boca Raton, FL, CRC Press.
4. Gilks W., Richardson, S., and Spiegelhalter D. (1996). Markov Chain Monte Carlo in Practice. London, Chapman and Hall.
5. Heckerman D., Geiger D., and Chickering D. 1995. Learning Bayesian networks: the combination of knowledge and statistical data. Machine Learning 20: 197-244.
6. Hinton G. and van Camp D. 1993. Keeping neural networks simple by minimizing the description length of the weights. In: Proceedings of the 6th Annual Workshop on Computational Learning Theory. New York, ACM Press.
7. Jordan M., Ghahramani Z., Jaakkola T., and Saul L. 1999. An introduction to variational methods in graphical models. In: Jordan M.I. (Ed.), Learning in Graphical Models. Cambridge, MA, MIT Press.
8. MacKay D. 1997. Ensemble learning for hidden Markov models. Unpublished manuscript. Department of Physics, University of Cambridge. Available on the web at http://wol.ra.phy. cam.ac.uk/mackay.
9. McCullagh P. and Nelder J. 1983. Generalized Linear Models. London, Chapman and Hall.
10. Nadal J-P. and Parga N. 1994. Duality between learning machines: A bridge between supervised and unsupervised learning. Neural Computation 6(3): 491-508.
11. Neal R. 1992. Connectionist learning of belief networks. Artificial Intelligence 56: 71-113.
12. Neal R. 1993. Probabilistic inference using Markov chain Monte Carlo methods. Technical report CRG-TR-93-1, University of Toronto.
13. Parisi G. 1988. Statistical field theory. Redwood City, CA, Addison-Wesley.
14. Rockafellar R. 1972. Convex Analysis. Princeton University Press.
15. Rustagi J. 1976. Variational Methods in Statistics. New York, Academic Press.
16. Saul L., Jaakkola T., and Jordan M. 1996. Mean field theory for sigmoid belief networks. Journal of Artificial Intelligence Research 4: 61-76.
17. Saul L. and Jordan M. 1996. Exploiting tractable substructures in intractable networks. In: Touretzky D.S., Mozer M.C., and Hasselmo M.E. (Eds.), Advances in Neural Information Processing Systems 8. Cambridge MA, MIT Press.
18. Spiegelhalter D. and Lauritzen S. 1990. Sequential updating of conditional probabilities on directed graphical structures. Networks 20: 579-605.
19. Thomas A., Spiegelhalter D., and Gilks W. 1992. BUGS: A program to perform Bayesian inference using Gibbs sampling. In: Bayesian Statistics 4. Clarendon Press.
20. Tipping M. 1999. Probabilistic visualisation of high-dimensional binary data. Advances in Neural Information Processing Systems 11.