Probabilistic reasoning in intelligent systems: networks of plausible inference
Probabilistic reasoning in intelligent systems: networks of plausible inference
Efficient learning in Boltzmann machines using linear response theory
Neural Computation
An introduction to variational methods for graphical models
Proceedings of the NATO Advanced Study Institute on Learning in graphical models
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
Bucket elimination: a unifying framework for probabilistic inference
Learning in graphical models
Improving the mean field approximation via the use of mixture distributions
Learning in graphical models
Tractable variational structures for approximating graphical models
Proceedings of the 1998 conference on Advances in neural information processing systems II
Neural Networks for Pattern Recognition
Neural Networks for Pattern Recognition
Variational methods for inference and estimation in graphical models
Variational methods for inference and estimation in graphical models
Neural Computation
Mean field theory for sigmoid belief networks
Journal of Artificial Intelligence Research
Mixture representations for inference and learning in Boltzmann machines
UAI'98 Proceedings of the Fourteenth conference on Uncertainty in artificial intelligence
IEEE Transactions on Neural Networks
Mean-field methods for a special class of belief networks
Journal of Artificial Intelligence Research
| Hi-index | 0.00 |
Intractable distributions present a common difficulty in inference within the probabilistic knowledge representation framework and variational methods have recently been popular in providing an approximate solution. In this article, we describe a perturbational approach in the form of a cumulant expansion which, to lowest order, recovers the standdard Kullback-Leibler variational bound. Higher-order terms describe corrections on the variational approach without incurring much further computational cost. The relationship to other perturbational approaches such as TAP is also elucidated. We demonstrate the method on a particular class of undirected graphical models, Boltzmann machines, for which our simulation results confirm improved accuracy and enhanced stability during learning.