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
Blocking Gibbs sampling in very large probabilistic expert systems
International Journal of Human-Computer Studies - Special issue: real-world applications of uncertain reasoning
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
Approximating posterior distributions in belief networks using mixtures
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
The structure of bayes networks for visual recognition
UAI '88 Proceedings of the Fourth Annual Conference on Uncertainty in Artificial Intelligence
Attractor Dynamics in Feedforward Neural Networks
Neural Computation
Mean field theory for sigmoid belief networks
Journal of Artificial Intelligence Research
Variational probabilistic inference and the QMR-DT network
Journal of Artificial Intelligence Research
Variational cumulant expansions for intractable distributions
Journal of Artificial Intelligence Research
Large deviation methods for approximate probabilistic inference
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
Reduction of computational complexity in Bayesian networksthrough removal of weak dependences
UAI'94 Proceedings of the Tenth international conference on Uncertainty in artificial intelligence
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The chief aim of this paper is to propose mean-field approximations for a broad class of Belief networks, of which sigmoid and noisy-or networks can be seen as special cases. The approximations are based on a powerful mean-field theory suggested by Plefka. We show that Saul, Jaakkola, and Jordan's approach is the first order approximation in Plefka's approach, via a variational derivation. The application of Plefka's theory to belief networks is not computationally tractable. To tackle this problem we propose new approximations based on Taylor series. Small scale experiments show that the proposed schemes are attractive.