Elements of information theory
Elements of information theory
Approximating posterior distributions in belief networks using mixtures
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
A revolution: belief propagation in graphs with cycles
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Improving the mean field approximation via the use of mixture distributions
Learning in graphical models
Statistics and Computing
Expectation Propagation for approximate Bayesian inference
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
Multimodal nonlinear filtering using Gauss-Hermite quadrature
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part III
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We propose a deterministic method to evaluate the integral of a positive function based on soft-binning functions that smoothly cut the integral into smaller integrals that are easier to approximate. In combination with mean-field approximations for each individual sub-part this leads to a tractable algorithm that alternates between the optimization of the bins and the approximation of the local integrals. We introduce suitable choices for the binning functions such that a standard mean field approximation can be extended to a split mean field approximation without the need for extra derivations. The method can be seen as a revival of the ideas underlying the mixture mean field approach. The latter can be obtained as a special case by taking soft-max functions for the binning.