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Variational methods continued

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If you have a question about this talk, please contact Richard Samworth.

I will continue Silvia’s discussion of variational methods, and try to answer some of the questions raised during her talk. We saw how mean field inference can give a lower bound on the log partition function Z. I will describe a general message passing framework based on alpha divergences, which has mean field and expectation propagation (EP, a generalisation of belief propagation for continuous random variables) as special cases, as well as tree reweighted belief propagation, which can give an upper bound on Z. EP will be shown to greatly outperform both Gibbs sampling and mean field on certain problems. If there is enough time I will present some work on choosing the optimal tree to approximate a loopy graph or even the right distribution over trees.

This talk is part of the Statistics Reading Group series.

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