Variational learning in nonlinear gaussian belief networks

Neural Computation

Volumn 11, Issue 1, 1999, Pages 193-213

  Frey, Brendan J ^a   Hinton, Geoffrey E ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY COLLEGE LONDON   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; ARTIFICIAL NEURAL NETWORK; AUTOMATED PATTERN RECOGNITION; DEPTH PERCEPTION; HANDWRITING; LEARNING; NONLINEAR SYSTEM; PATTERN RECOGNITION; PHYSIOLOGY; STATISTICS;

DEPTH PERCEPTION; HANDWRITING; LEARNING; NEURAL NETWORKS (COMPUTER); NONLINEAR DYNAMICS; PATTERN RECOGNITION, AUTOMATED; PATTERN RECOGNITION, VISUAL; STOCHASTIC PROCESSES;

EID: 0032603958     PISSN: 08997667     EISSN: None     Source Type: Journal    
DOI: 10.1162/089976699300016872     Document Type: Article

References (27)

1. Amari, S.-I. (1985). Differential-geometrical methods in statistics. New York: Springer-Verlag.
2. Amari, S.-I., Cichocki, A., & Yang, H. (1996). A new learning algorithm for blind signal separation. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems, 8. Cambridge, MA: MIT Press.
3. Becker, S., & Hinton, G. E. (1992). A self-organizing neural network that discovers surfaces in random-dot stereograms. Nature, 355, 161-163.
4. Bell, A. J., & Sejnowski, T. J. (1995). An information maximization approach to blind separation and blind deconvolution. Neural Computation, 7, 1129-1159.
5. Comon, P., Jutten, C., & Herault, J. (1991). Blind separation of sources. Signal Processing, 24, 11-20.
6. Dayan, P., Hinton, G. E., Neal, R. M., & Zemel, R. S. (1995). The Helmholtz machine. Neural Computation, 7, 889-904.
7. Dayan, P., & Zemel, R. S. (1995). Competition and multiple cause models. Neural Computation, 7, 565-579.
8. Everitt, B. S. (1984). An introduction to latent variable models. New York: Chapman and Hall.
9. Frey, B. J. (1997a). Continuous sigmoidal belief networks trained using slice sampling. In M. C. Mozer, M. I. Jordan, & T. Petsche (Eds.), Advances in neural information processing systems, 9. Cambridge, MA: MIT Press. Available online at: http://www.cs.utoronto.ca/~frey.
10. Frey, B. J. (1997b). Variational inference for continuous sigmoidal Bayesian networks. In Sixth International Workshop on Artificial Intelligence and Statistics.
11. Frey, B. J. (1998). Graphical models for machine learning and digital communication. Cambridge, MA: MIT Press. Available online at: http://mitpress.mit.edu/book-home.tcl?isbn=026206202X.
12. Hinton, G. E., Dayan, P., Frey, B. J., & Neal, R. M. (1995). The wake-sleep algorithm for unsupervised neural networks. Science, 268, 1158-1161.
13. Hinton, G. E., & Ghahramani, Z. (1997). Generative models for discovering sparse distributed representations. Philosophical Transactions of the Royal Society of London B, 352, 1177-1190.
14. Hinton, G. E., Sallans, B., & Ghahramani, Z. (1998). A hierarchical community of experts. In M. I. Jordan (Ed.), Learning and inference in graphical models. Norwell, MA: Kluwer.
15. Hinton, G. E., & Sejnowski, T. J. (1986). Learning and relearning in Boltzmann machines. In D. E. Rumelhart & J. L. McClelland (Eds.), Parallel distributed processing: Explorations in the microstructure of cognition (vol. 1, pp. 282-317). Cambridge, MA: MIT Press.
16. Hull, J. J. (1994). A database for handwritten text recognition research. IEEE Transactions on Pattern Analysis and Machine Intelligence, 16, 550-554.
17. Jaakkola, T. S., & Jordan, M. I. (1998). Approximating posteriors via mixture models. In M. I. Jordan (Ed.), Learning and inference in graphical models. Norwell MA: Kluwer.
18. Jaakkola, T., Saul, L. K., & Jordan, M. I. (1996). Fast learning by bounding like-lihoods in sigmoid type belief networks. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in neural information processing systems, 8. Cambridge, MA: MIT Press.
19. Lewicki, M. S., & Sejnowski, T. J. (1998). Learning nonlinear overcomplete representations for efficient coding. In M. I. Jordan, M. I. Kearns, & S. A. Solla (Eds.), Advances in neural information processing systems, 10. Cambridge, MA: MIT Press.
20. MacKay, D. J. C. (1997). Maximum likelihood and covariant algorithms for independent component analysis. Unpublished manuscript. Available online at: http://wol.ra.phy.cam.ac.uk/mackay.
21. Neal, R. M. (1992). Connectionist learning of belief networks. Artificial Intelligence, 56, 71-113.
22. Neal, R. M., & Hinton, G. E. (1993). A new view of the EM algorithm that justifies incremental and other variants. Unpublished manuscript. Available via FTP at: ftp://ftp.cs.utoronto.ca/pub/radford/em.ps.Z.
23. Olshausen, B. A., & Field, D. J. (1996). Emergence of simple-cell receptive-field properties by learning a sparse code for natural images. Nature, 381, 607-609.
24. Pearl, J. (1988). Probabilistic reasoning in intelligent systems. San Mateo, CA: Morgan Kaufmann.
25. Rasmussen, C. E., Neal, R. M., Hinton, G. E., van Camp, D., Revow, M., Ghahramani, Z., Kustra, R., & Tibshirani, R. (1996). The DELVE manual. Toronto: University of Toronto. Available online at: http://www.cs.utoronto.ca/~delve.
26. Rubin, D., & Thayer, D. (1982). EM algorithms for ML factor analysis. Psychometrika, 47, 69-76.
27. Saul, L. K., Jaakkola, T., & Jordan, M. I. (1996). Mean field theory for sigmoid belief networks. Journal of Artificial Intelligence Research, 4, 61-76.