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Bayesian Statistics 9$
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José M. Bernardo, M. J. Bayarri, James O. Berger, A. P. Dawid, David Heckerman, Adrian F. M. Smith, and Mike West

Print publication date: 2011

Print ISBN-13: 9780199694587

Published to Oxford Scholarship Online: January 2012

DOI: 10.1093/acprof:oso/9780199694587.001.0001

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Approximating Max‐Sum‐Product Problems using Multiplicative Error Bounds

Approximating Max‐Sum‐Product Problems using Multiplicative Error Bounds

Chapter:
(p.439) Approximating Max‐Sum‐Product Problems using Multiplicative Error Bounds
Source:
Bayesian Statistics 9
Author(s):

Christopher Meek

Ydo Wexler

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199694587.003.0015

We describe the Multiplicative Approximation Scheme (MAS) for approximate inference in multiplicative models. We apply this scheme to develop the DynaDecomp approximation algorithm. This algorithm can be used to obtain bounded approximations for various types of max‐sum‐product problems including the computation of the log probability of evidence, the log‐partition function, Most Probable Explanation (MPE) and maximum a posteriori probability (MAP) inference problems. We demonstrate that this algorithm yields bounded approximations superior to existing methods using a variety of large graphical models.

Keywords:   Approximate inference, graphical models, max‐sum‐product, sum‐product

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