Abstract
We develop a new extension to the Mean-Field approximation for inference in graphical models which has advantages over other approximation schemes which have been proposed. The method is economical in its use of variational parameters and the approximating conditional distribution can be specified with direct reference to the dependence structure of the variables in the graphical model. We apply the method to sigmoid belief networks.
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Jordan, M. I., Ghahramani, Z., Jaakkola, T. and Saul, L. K.: An introduction to variational methods for graphical models, in: Jordan, M. I. (ed.), Learning in Graphical models, Kluwer, 1998, pp. 105–161.
Saul, L. K., Jaakkola, T. and Jordan, M. I.: Mean-Field theory for sigmoid belief networks, J. Artif. Intel. Res. 4 (1996), 61–76.
Saul, L. K. and Jordan, M. I.: Exploiting tractable substructures in intractable networks, in: Touretzky, D. S., Mozer, M. C. and Hasselmo, M. E. (eds), Advances in Neural Information Processing Systems, Vol. 8, MIT Press, Cambridge, MA, 1996, pp. 486–492.
Bishop, C. M., Lawrence, N., Jaakkola, T. and Jordan, M. I.: Approximating posterior distributions in belief networks using mixtures, in: Jordan, M. I., Kearns, M. J. and Solla, S. A. (eds), Advances of Neural Information Processing Systems, Vol. 10, MIT Press, Cambridge, MA, 1998, pp. 416–422.
Bahadur, R. R.: A representation of the joint distribution of responses to n dichotomous items, in: Solomon, H. (ed.), Studies in Item Analysis and Prediction, Stanford University Press, Stanford, 1961, pp. 158–168.
Numerical Algorithms Group, The NAG Workstation Library Handbook-Release 1, 1986.
Jaakkola, T. S. and Jordan, M. I.: Computing upper and lower bounds on likelihoods in intractable networks, Massachusetts Institute of Technology, C.B.C.L. Memo No.136/A.I. Memo No.1571, 1996.
Humphreys, K. and Titterington, D. M.: The exploration of new methods for learning in binary Boltzmann machines, in: Heckerman, D. and Whittaker, J. (eds), Proc. Seventh Internat. Workshop on Artificial Intelligence and Statistics, Morgan Kaufmann, San Francisco, CA, 1999, pp. 209–214.
Kappen, H. J. and Rodriguez, F. B.: Efficient learning in Boltzmann machines using linear response theory, Neural Comput. 10 (1998), 1137–1156.
Dempster, A. P., Laird, N. M. and Rubin, D. B.: Maximum likelihood from incomplete data via the EM algorithm (with discussion), J. Roy. Statistical Soc. B, 39 (1977), 1–38.
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Humphreys, K., Titterington, D.M. Improving the Mean-Field Approximation in Belief Networks Using Bahadur's Reparameterisation of the Multivariate Binary Distribution. Neural Processing Letters 12, 183–197 (2000). https://doi.org/10.1023/A:1009617914949
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DOI: https://doi.org/10.1023/A:1009617914949