Approximate inference using unimodular graphs in dual decomposition

We use the property of unimodular functions to perform approximate inference with dual decomposition in binary labeled graphs. Exact inference is possible for a subclass of binary labeled graphs that have unimodular functions. We call such graphs unimodular graphs. These are graphs where the submodular and nonsubmodular edges follow a specific pattern– essentially that an isomorphism or ”flipping” exists to a fully submodular graph. Examples of unimodular graphs include tree-structured graphs, submodular graphs, and bipartite graphs with all non-submodular edges. We investigate the use of unimodular graphs in dual decomposition, based on different decomposition strategies. Experimentally, for image segmentation problems, we find that decomposition using unimodular graphs outperform traditional tree-based dual decomposition. Dual decomposition is also more easily parallelizable.