PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Understanding and Improving Belief Propagation
Joris Mooij
(2008) PhD thesis, Radboud University Nijmegen.

Abstract

In this thesis we have tried to better understand and improve upon Belief Propagation (BP), a popular approximate inference method that performs surprisingly well on many problems. It has been rediscovered many times in different fields and is therefore known under different names: ``Belief Propagation'', ``Loopy Belief Propagation'', the ``Sum-Product Algorithm'' and the ``Bethe-Peierls approximation''. BP is an iterative fixed point algorithm that minimises the Bethe free energy. It yields exact results if the underlying graphical model has no loops. If the graphical model does have loops, the BP results are approximate but can be surprisingly accurate. However, if variables become highly dependent, the error made by BP can become significant. In some cases, BP does not even converge anymore. The results in this thesis have contributed to a better understanding of these issues. In addition, we introduced a method that improves the accuracy of BP by taking into account the influence of loops in the graphical model. Finally, we proposed a method to calculate exact bounds on marginal probabilities, which was inspired by BP.

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EPrint Type:Thesis (PhD)
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:4737
Deposited By:Joris Mooij
Deposited On:24 March 2009