Abstract
Mean field methods provide computationally efficient approximations to posterior probability distributions for graphical models. Simple mean field methods make a completely factorized approximation to the posterior, which is unlikely to be accurate when the posterior is multimodal. Indeed, if the posterior is multi-modal, only one of the modes can be captured. To improve the mean field approximation in such cases, we employ mixture models as posterior approximations, where each mixture component is a factorized distribution. We describe efficient methods for optimizing the Parameters in these models.
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References
Bishop, C., Lawrence, N., Jaakkola, T. S., & Jordan, M. I. Approximating posterior distributions in belief networks using mixtures. In M. I. Jordan, M. J. Kearns, & S. A. Solla, Advances in Neural Information Processing Systems 10, MIT Press, Cambridge MA (1998).
Ghahramani, Z. & Jordan, M. I. Factorial Hidden Markov models. In D. S. Touretzky, M. C. Mozer, & M. E. Hasselmo (Eds.), Advances in Neural Information Processing Systems 8, MIT Press, Cambridge MA (1996).
Neal, R. Connectionist learning of belief networks, Artificial Intelligence, 56: 71–113 (1992).
Parisi, G. Statistical Field Theory. Addison-Wesley: Redwood City (1988).
Peterson, C. & Anderson, J. R. A mean field theory learning algorithm for neural networks. Complex Systems1: 995–1019 (1987).
Saul, L. K., Jaakkola, T. S., & Jordan, M. I. Mean field theory for sigmoid belief networks. Journal of Artificial Intelligence Research, 4: 61–76 (1996).
Saul, L. K. & Jordan, M. I. Exploiting tractable substructures in intractable networks. In D. S. Touretzky, М. C. Mozer, & M. E. Hasselmo (Eds.), Advances in Neural Information Processing Systems 8, MIT Press, Cambridge MA (1996).
Shwe, М. A., Middleton, B., Beckerman, D. E., Henrion, M., Horvitz, E. J., Lehmann, H. P., & Cooper, G. F. Probabilistic diagnosis using a reformulation of the INTERNIST1/QMR knowledge base. Meth. Inform. Med. 30: 241–255 (1991).
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© 1998 Springer Science+Business Media Dordrecht
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Jaakkola, T.S., Jordan, M.I. (1998). Improving the Mean Field Approximation Via the Use of Mixture Distributions. In: Jordan, M.I. (eds) Learning in Graphical Models. NATO ASI Series, vol 89. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-5014-9_6
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DOI: https://doi.org/10.1007/978-94-011-5014-9_6
Publisher Name: Springer, Dordrecht
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