Bounds on marginal probability distributions

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.

• Type: Conference
• Year: 2008
• Where: NIPS
• Authors: Joris M. Mooij, Hilbert J. Kappen
• Keywords: Factor Graph, Information Technology, Marginal Probability Distribution, NIPS 2008, Probability Distribution