Tighter Linear Program Relaxations for High Order Graphical Models

Elad Mezuman, Daniel Tarlow, Amir Globerson, Yair Weiss
Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, PMLR R11:530-539, 2013.

Abstract

Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of ap- proaches to inference in these models, nearly all of them amount to solving a linear pro- gram (LP) relaxation with unary consistency constraints between the HOP and the indi- vidual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus de- sirable to look for more accurate ways of per- forming inference. In this work, we study the LP relaxations that result from enforcing ad- ditional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the re- laxations that arise in standard approaches, and we develop practical and efficient mes- sage passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challeng- ing problems that include a combination of low order and high order terms.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR11-mezuman13a, title = {Tighter Linear Program Relaxations for High Order Graphical Models}, author = {Mezuman, Elad and Tarlow, Daniel and Globerson, Amir and Weiss, Yair}, booktitle = {Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence}, pages = {530--539}, year = {2013}, editor = {Nicholson, Ann and Smyth, Padhraic}, volume = {R11}, series = {Proceedings of Machine Learning Research}, month = {12--14 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r11/main/assets/mezuman13a/mezuman13a.pdf}, url = {https://proceedings.mlr.press/r11/mezuman13a.html}, abstract = {Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of ap- proaches to inference in these models, nearly all of them amount to solving a linear pro- gram (LP) relaxation with unary consistency constraints between the HOP and the indi- vidual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus de- sirable to look for more accurate ways of per- forming inference. In this work, we study the LP relaxations that result from enforcing ad- ditional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the re- laxations that arise in standard approaches, and we develop practical and efficient mes- sage passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challeng- ing problems that include a combination of low order and high order terms.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Tighter Linear Program Relaxations for High Order Graphical Models %A Elad Mezuman %A Daniel Tarlow %A Amir Globerson %A Yair Weiss %B Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2013 %E Ann Nicholson %E Padhraic Smyth %F pmlr-vR11-mezuman13a %I PMLR %P 530--539 %U https://proceedings.mlr.press/r11/mezuman13a.html %V R11 %X Graphical models with High Order Potentials (HOPs) have received considerable interest in recent years. While there are a variety of ap- proaches to inference in these models, nearly all of them amount to solving a linear pro- gram (LP) relaxation with unary consistency constraints between the HOP and the indi- vidual variables. In many cases, the resulting relaxations are loose, and in these cases the results of inference can be poor. It is thus de- sirable to look for more accurate ways of per- forming inference. In this work, we study the LP relaxations that result from enforcing ad- ditional consistency constraints between the HOP and the rest of the model. We address theoretical questions about the strength of the resulting relaxations compared to the re- laxations that arise in standard approaches, and we develop practical and efficient mes- sage passing algorithms for optimizing the LPs. Empirically, we show that the LPs with additional consistency constraints lead to more accurate inference on some challeng- ing problems that include a combination of low order and high order terms. %Z Reissued by PMLR on 04 October 2026.
APA
Mezuman, E., Tarlow, D., Globerson, A. & Weiss, Y.. (2013). Tighter Linear Program Relaxations for High Order Graphical Models. Proceedings of the 29th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R11:530-539 Available from https://proceedings.mlr.press/r11/mezuman13a.html. Reissued by PMLR on 04 October 2026.

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