Graph Cuts Is a Max-Product Algorithm
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
Text
Tarlow et al. "Graph Cuts Is a Max-Product Algorithm." Conference on Uncertainty in Artificial Intelligence, 2011.Markdown
[Tarlow et al. "Graph Cuts Is a Max-Product Algorithm." Conference on Uncertainty in Artificial Intelligence, 2011.](https://mlanthology.org/uai/2011/tarlow2011uai-graph/)BibTeX
@inproceedings{tarlow2011uai-graph,
title = {{Graph Cuts Is a Max-Product Algorithm}},
author = {Tarlow, Daniel and Givoni, Inmar E. and Zemel, Richard S. and Frey, Brendan J.},
booktitle = {Conference on Uncertainty in Artificial Intelligence},
year = {2011},
pages = {671-680},
url = {https://mlanthology.org/uai/2011/tarlow2011uai-graph/}
}