Efficient Learning of Structured Predictors in General Graphical Models

In this paper we derive an efficient message-passing algorithm to learn the parameters of structured predictors in general graphical models. We define the extended log-loss, which relates the log-loss of CRFs and the hinge-loss of structured SVMs through a temperature parameter. We then investigate the primal and dual properties of the extended log-loss, showing that the dual programs of both CRFs and structured SVMs perform moment matching using different selection rules. Utilizing the graphical models of the predictors, we describe a low dimensional extended log-loss formulation, which is derived from pseudo moment matching and a fractional entropy approximation selection rule in the dual setting. We propose an efficient message-passing algorithm that is guaranteed to converge to the optimum of the low dimensional primal and dual programs. Unlike many of the existing approaches, this allows us to learn efficiently high-order graphical models, over regions of any size, and very large number of parameters. We demonstrate the effectiveness of our approach, while presenting state-of-the-art results in stereo estimation, semantic segmentation, shape reconstruction, and indoor scene understanding.