Understanding and improving belief propagation

摘要: The research reported in this thesis focuses on approximation techniques for inference graphical models. Approximate can be dTefined as the task of calculating approximations certain probabilities large, complexprobabilistic models, such Bayesian networks, Markov random fields or Ising spin systems (which are all special cases models). We have focussed models with variables that a finite number possible values. Calculating these is simple principle, but computationally hard practice, because it requires summation over an exponential terms. However, practical relevance enormous: application areas include genetic linkage analysis, medical diagnosis, expert systems, error correcting codes, speech recognition, computer vision and many more. Because one interested cannot always calculated exactly (given limited amount computation time), often uses approximate methods, which use less time only give quantities interest. In thesis, we tried to better understand improve upon Belief Propagation (BP), popular method performs surprisingly well problems. It also known 'Loopy Propagation', 'Sum-Product Algorithm' 'Bethe-Peierls approximation'. BP yields exact results if underlying model has no loops. general, accurate. become highly dependent, made by significant. some cases, does not even converge anymore. Our contributed understanding issues. addition, introduced improves accuracy taking into account influence loops model. Finally, proposed calculate bounds marginal probabilities, was inspired