Structured Prediction by Joint Kernel Support Estimation
Christoph Lampert and Matthew Blaschko
Discriminative techniques, such as conditional random fields (CRFs) or structure aware maximum-margin techniques (maximum margin Markov networks (M3N), structured output support vector machines (S-SVM)), are state-of-the-art in the prediction of structured data. However, to achieve good results these techniques require complete and reliable ground truth, which is not always available in realistic problems. Furthermore, training either CRFs or margin-based techniques is computationally costly, because the runtime of current training methods depends not only on the size of the training set but also on properties of the output space to which the training samples are assigned. We propose an alternative model for structured output prediction, Joint Kernel Support Estimation (JKSE), which is rather generative in nature as it relies on estimating the joint probability density of samples and labels in the training set. This makes it tolerant against incomplete or incorrect labels and also opens the possibility of learning in situations where more than one output label can be considered correct. At the same time, we avoid typical problems of generative models as we do not attempt to learn the full joint probability distribution, but we model only its support in a joint reproducing kernel Hilbert space. As a consequence, JKSE training is possible by an adaption of the classical one-class SVM procedure. The resulting optimization problem is convex and efficiently solvable even with tens of thousands of training examples. A particular advantage of JKSE is that the training speed depends only on the size of the training set, and not on the total size of the label space. No inference step during training is required (as M3N and S-SVM would) nor do we have calculate a partition function (as CRFs do). Experiments on realistic data show that, for suitable kernel functions, our method works efficiently and robustly in situations that discriminative techniques have problems with or that are computationally infeasible for them.