Interpreting Graph Cuts as a Max-Product Algorithm

Daniel Tarlow, Inmar E. Givoni, Richard S. Zemel, Brendan J. Frey
Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, PMLR R9:742-753, 2011.

Abstract

The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008). In this work, we show that under a particular scheduling and damping scheme, MP is equivalent to graph cuts, and thus optimal. We explain the apparent contradiction by showing that with proper scheduling and damping, MP always converges to an optimal fixed point. Thus, the canonical counterexample only shows the suboptimality of MP with a particular suboptimal choice of schedule and damping. With proper choices, MP is optimal.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR9-tarlow11a, title = {Interpreting Graph Cuts as a Max-Product Algorithm}, author = {Tarlow, Daniel and Givoni, Inmar E. and Zemel, Richard S. and Frey, Brendan J.}, booktitle = {Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence}, pages = {742--753}, year = {2011}, editor = {Cozman, Fabio and Pfeffer, Avi}, volume = {R9}, series = {Proceedings of Machine Learning Research}, month = {14--17 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r9/main/assets/tarlow11a/tarlow11a.pdf}, url = {https://proceedings.mlr.press/r9/tarlow11a.html}, abstract = {The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008). In this work, we show that under a particular scheduling and damping scheme, MP is equivalent to graph cuts, and thus optimal. We explain the apparent contradiction by showing that with proper scheduling and damping, MP always converges to an optimal fixed point. Thus, the canonical counterexample only shows the suboptimality of MP with a particular suboptimal choice of schedule and damping. With proper choices, MP is optimal.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Interpreting Graph Cuts as a Max-Product Algorithm %A Daniel Tarlow %A Inmar E. Givoni %A Richard S. Zemel %A Brendan J. Frey %B Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2011 %E Fabio Cozman %E Avi Pfeffer %F pmlr-vR9-tarlow11a %I PMLR %P 742--753 %U https://proceedings.mlr.press/r9/tarlow11a.html %V R9 %X The maximum a posteriori (MAP) configuration of binary variable models with submodular graph-structured energy functions can be found efficiently and exactly by graph cuts. Max-product belief propagation (MP) has been shown to be suboptimal on this class of energy functions by a canonical counterexample where MP converges to a suboptimal fixed point (Kulesza & Pereira, 2008). In this work, we show that under a particular scheduling and damping scheme, MP is equivalent to graph cuts, and thus optimal. We explain the apparent contradiction by showing that with proper scheduling and damping, MP always converges to an optimal fixed point. Thus, the canonical counterexample only shows the suboptimality of MP with a particular suboptimal choice of schedule and damping. With proper choices, MP is optimal. %Z Reissued by PMLR on 04 October 2026.
APA
Tarlow, D., Givoni, I.E., Zemel, R.S. & Frey, B.J.. (2011). Interpreting Graph Cuts as a Max-Product Algorithm. Proceedings of the 27th Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R9:742-753 Available from https://proceedings.mlr.press/r9/tarlow11a.html. Reissued by PMLR on 04 October 2026.

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