Negative Tree Reweighted Belief Propagation

Qiang Liu, Alexander Ihler
Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, PMLR R8:339-346, 2010.

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 na\"{}{ı}ve and structured mean field approximations), which it includes as a limiting case.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR8-liu10a, title = {Negative Tree Reweighted Belief Propagation}, author = {Liu, Qiang and Ihler, Alexander}, booktitle = {Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence}, pages = {339--346}, year = {2010}, editor = {Grünwald, Peter and Spirtes, Peter}, volume = {R8}, series = {Proceedings of Machine Learning Research}, month = {08--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r8/main/assets/liu10a/liu10a.pdf}, url = {https://proceedings.mlr.press/r8/liu10a.html}, 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 na\"{}{ı}ve and structured mean field approximations), which it includes as a limiting case.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Negative Tree Reweighted Belief Propagation %A Qiang Liu %A Alexander Ihler %B Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2010 %E Peter Grünwald %E Peter Spirtes %F pmlr-vR8-liu10a %I PMLR %P 339--346 %U https://proceedings.mlr.press/r8/liu10a.html %V R8 %X 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 na\"{}{ı}ve and structured mean field approximations), which it includes as a limiting case. %Z Reissued by PMLR on 04 October 2026.
APA
Liu, Q. & Ihler, A.. (2010). Negative Tree Reweighted Belief Propagation. Proceedings of the 26th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R8:339-346 Available from https://proceedings.mlr.press/r8/liu10a.html. Reissued by PMLR on 04 October 2026.

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