Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Connectionist learning of belief networks
Artificial Intelligence
Boltzmann machine learning using mean field theory and linear response correction
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
A view of the EM algorithm that justifies incremental, sparse, and other variants
Learning in graphical models
Mean field theory for sigmoid belief networks
Journal of Artificial Intelligence Research
Computing upper and lower bounds on likelihoods in intractable networks
UAI'96 Proceedings of the Twelfth international conference on Uncertainty in artificial intelligence
Journal of Artificial Intelligence Research
Computer generated higher order expansions
UAI'02 Proceedings of the Eighteenth conference on Uncertainty in artificial intelligence
A generalized mean field algorithm for variational inference in exponential families
UAI'03 Proceedings of the Nineteenth conference on Uncertainty in Artificial Intelligence
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We present a method to bound the partition function of a Boltzmann machine neural network with any odd-order polynomial. This is a direct extension of the mean-field bound, which is first order. We show that the third-order bound is strictly better than mean field. Additionally, we derive a third-order bound for the likelihood of sigmoid belief networks. Numerical experiments indicate that an error reduction of a factor of two is easily reached in the region where expansion-based approximations are useful.