Ben Taskar, Simon Lacoste-Julien, Michael Jordan
We present a simple and scalable algorithm for large-margin estima- tion of structured models, including an important class of Markov net- works and combinatorial models. We formulate the estimation problem as a convex-concave saddle-point problem and apply the extragradient method, yielding an algorithm with linear convergence using simple gra- dient and projection calculations. The projection step can be solved us- ing combinatorial algorithms for min-cost quadratic ﬂow. This makes the approach an efﬁcient alternative to formulations based on reductions to a quadratic program (QP). We present experiments on two very different structured prediction tasks: 3D image segmentation and word alignment, illustrating the favorable scaling properties of our algorithm.