High Order Regularization for Semi-Supervised Learning of Structured Output Problems
Yujia Li, Rich Zemel · 2014
Semi-supervised learning, which uses unlabeled data to help learn a discriminative model, is espe-cially important for structured output problems, as considerably more effort is needed to label its multi-dimensional outputs versus standard single output problems. We propose a new max-margin framework for semi-supervised structured output learning, that allows the use of powerful discrete optimization algorithms and high order regular-izers defined directly on model predictions for the unlabeled examples. We show that our frame-work is closely related to Posterior Regulariza-tion, and the two frameworks optimize special cases of the same objective. The new framework is instantiated on two image segmentation tasks, using both a graph regularizer and a cardinality regularizer. Experiments also demonstrate that this framework can utilize unlabeled data from a different source than the labeled data to signifi-cantly improve performance while saving label-ing effort. 1.