Uncertainty in Artificial Intelligence
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Negative Tree Reweighted Belief Propagation
Qiang Liu, Alexander Ihler
Abstract:
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound counterpart to the tree-reweighted belief propagation algorithm, which uses a convex combination of spanning trees with positive weights to provide corresponding upper bounds. We develop algorithms to optimize and tighten the lower bounds over the non-convex set of valid parameter values. Our algorithm generalizes mean field approaches (including naive and structured mean field approximations), which it includes as a limiting case.
Keywords:
Pages: 332-339
PS Link:
PDF Link: /papers/10/p332-liu.pdf
BibTex:
@INPROCEEDINGS{Liu10,
AUTHOR = "Qiang Liu and Alexander Ihler",
TITLE = "Negative Tree Reweighted Belief Propagation",
BOOKTITLE = "Proceedings of the Twenty-Sixth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-10)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2010",
PAGES = "332--339"
}


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