Efficient training for pairwise or higher order CRFs via dual decomposition

We present a very general algorithmic framework for structured prediction learning that is able to efficiently handle both pairwise and higher-order discrete MRFs/CRFs
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. It relies on a dual decomposition approach that has been recently proposed for MRF optimization. By properly combining this approach with a max-margin method, our framework manages to reduce the training of a complex high-order MRF to the parallel training of a series of simple slave MRFs that are much easier to handle. This leads to an extremely efficient and general learning scheme. Furthermore, the proposed framework can yield learning algorithms of increasing accuracy since it naturally allows a hierarchy of convex relaxations to be used for MRF inference within a max-margin learning approach. It also offers extreme flexibility and can be easily adapted to take advantage of any special structure of a given class of MRFs. Experimental results demonstrate the great effectiveness of our method.