Uncertainty in Artificial Intelligence
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Understanding the Bethe Approximation: When and How can it go Wrong?
Adrian Weller, Kui Tang, Tony Jebara, David Sontag
Abstract:
Belief propagation is a remarkably effective tool for inference, even when applied to networks with cycles. It may be viewed as a way to seek the minimum of the Bethe free energy, though with no convergence guarantee in general. A variational perspective shows that, compared to exact inference, this minimization employs two forms of approximation: (i) the true entropy is approximated by the Bethe entropy, and (ii) the minimization is performed over a relaxation of the marginal polytope termed the local polytope. Here we explore when and how the Bethe ap- proximation can fail for binary pairwise models by examining each aspect of the approximation, deriving results both analytically and with new experimental methods.
Keywords:
Pages: 868-877
PS Link:
PDF Link: /papers/14/p868-weller.pdf
BibTex:
@INPROCEEDINGS{Weller14,
AUTHOR = "Adrian Weller and Kui Tang and Tony Jebara and David Sontag",
TITLE = "Understanding the Bethe Approximation: When and How can it go Wrong?",
BOOKTITLE = "Proceedings of the Thirtieth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-14)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2014",
PAGES = "868--877"
}


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