Idea Transcript
MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com
Understanding Belief Propagation and its Generalizations
Jonathan S. Yedidia, William T. Freeman, and Yair Weiss
TR2001-22
November 2001
Abstract ”Inference” problems arise in statistical physics, computer vision, error-correcting coding theory, and AI. We explain the principles behind the belief propagation (BP) algorithm, which is an efficient way to solve inference problems based on passing local messages. We develop a unified approach with examples, notation, and graphical models borrowed from the relevant disciplines.We explain the close connection between the BP algorithm and the Bethe approximation of statistical physics. In particular, we show that BP can only converge to a fixed point that is also a stationary point of the Bethe approximation to the free energy. This result helps explain the successes of the BP algorithm and enables connections to be made with variational approaches to approximate inference. Delivered in the the ’Destinguished Lecture’ track at the 2001 International Joint Conference on Artificial Intelligence in August 2001. To be published in a book collecting those lectures.
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Delivered in the “Distinguished Lecture” track at the 2001 International Joint Conference on Artificial Intelligence in August 2001. To be published in a book collecting those lectures. First Draft August 2001. Final Draft January 2002.
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