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Conference Paper

Bounds on marginal probability distributions

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Mooij,  JM
Department Empirical Inference, Max Planck Institute for Biological Cybernetics, Max Planck Society;
Max Planck Institute for Biological Cybernetics, Max Planck Society;

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Citation

Mooij, J., & Kappen, B. (2009). Bounds on marginal probability distributions. In D. Koller, D. Schuurmans, Y. Bengio, & L. Bottou (Eds.), Advances in neural information processing systems 21 (pp. 1105-1112). Red Hook, NY, USA: Curran.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-C46F-F
Abstract
We propose a novel bound on single-variable marginal probability distributions in factor graphs with discrete variables. The bound is obtained by propagating local bounds (convex sets of probability distributions) over a subtree of the factor graph, rooted in the variable of interest. By construction, the method not only bounds the exact marginal probability distribution of a variable, but also its approximate Belief Propagation marginal ("belief"). Thus, apart from providing a practical means to calculate bounds on marginals, our contribution also lies in providing a better understanding of the error made by Belief Propagation. We show that our bound outperforms the state-of-the-art on some inference problems arising in medical diagnosis.