PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

Bounds on marginal probability distributions
Joris Mooij and Bert Kappen
Advances in Neural Information Processing Systems Volume 21, pp. 1105-1112, 2009.


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.

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EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Theory & Algorithms
ID Code:4749
Deposited By:Joris Mooij
Deposited On:24 March 2009