Regularizing Structured Classifier with Conditional Probabilistic Constraints for Semi-supervised Learning

Constraints have been shown as an effective way to incorporate unlabeled data for semi-supervised structured classification. We recognize that, constraints are often conditional and probabilistic; moreover, a constraint can have its condition depend on either just observations (which we call x-type constraint) or even hidden variables (which we call y-type constraint). We wish to design a constraint formulation that can flexibly model the constraint probability for both x-type and y-type constraints, and later use it to regularize general structured classifiers for semi-supervision. Surprisingly, none of the existing models have such a constraint formulation. Thus in this paper, we propose a new conditional probabilistic formulation for modeling both x-type and y-type constraints. We also recognize the inference complication for y-type constraint, and propose a systematic selective evaluation approach to efficiently realize the constraints. Finally, we evaluate our model in three applications, including named entity recognition, part-of-speech tagging and entity information extraction, with totally nine data sets. We show that our model is generally more accurate and efficient than the state-of-the-art baselines. Our code and data are available at https://bitbucket.org/vwz/cikm2016-cpf/.