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Bounds on marginal probability distributions

2009

Conference Paper

ei


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.

Author(s): Mooij, JM. and Kappen, B.
Book Title: Advances in neural information processing systems 21
Journal: Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008
Pages: 1105-1112
Year: 2009
Month: June
Day: 0
Editors: Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou
Publisher: Curran

Department(s): Empirical Inference
Bibtex Type: Conference Paper (inproceedings)

Event Name: Twenty-Second Annual Conference on Neural Information Processing Systems (NIPS 2008)
Event Place: Vancouver, BC, Canada

Address: Red Hook, NY, USA
Digital: 0
ISBN: 978-1-605-60949-2
Language: en
Organization: Max-Planck-Gesellschaft
School: Biologische Kybernetik

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BibTex

@inproceedings{5407,
  title = {Bounds on marginal probability distributions},
  author = {Mooij, JM. and Kappen, B.},
  journal = {Advances in neural information processing systems 21 : 22nd Annual Conference on Neural Information Processing Systems 2008},
  booktitle = {Advances in neural information processing systems 21},
  pages = {1105-1112},
  editors = {Koller, D. , D. Schuurmans, Y. Bengio, L. Bottou},
  publisher = {Curran},
  organization = {Max-Planck-Gesellschaft},
  school = {Biologische Kybernetik},
  address = {Red Hook, NY, USA},
  month = jun,
  year = {2009},
  month_numeric = {6}
}