Minimizing Sparse High-Order Energies by Submodular Vertex-Cover

Andrew Delong, Olga Veksler, Anton Osokin, Yuri Boykov

In Neural Information Processing Systems (NIPS), Lake Tahoe, USA, December, 2012.


Inference in high-order graphical models has become important in recent years. Several approaches are based, for example, on generalized message-passing, or on transformation to a pairwise model with extra ‘auxiliary’ variables. We focus on a special case where a much more efficient transformation is possible. Instead of adding variables, we transform the original problem into a comparatively small instance of submodular vertex-cover. These vertex-cover instances can then be attacked by existing algorithms (e.g. belief propagation, QPBO), where they often run 4–15 times faster and find better solutions than when applied to the original problem. We evaluate our approach on synthetic data, then we show applications within a fast hierarchical clustering and model-fitting framework.

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