Large-Margin Structured Prediction via Linear Programming

This paper presents a novel learning algorithm for structured classification, where the task is to predict multiple and interacting labels (multilabel) for an input object. The problem of finding a large-margin separation between correct multilabels and incorrect ones is formulated as a linear program. Instead of explicitly writing out the entire problem with an exponentially large constraint set, the linear program is solved iteratively via column generation. In this case, the process of generating most violated constraints is equivalent to searching for highest-scored misclassified incorrect multilabels, which can be easily achieved by decoding the structure based on current estimations. In addition, we also explore the integration of column generation and an extragradient method for linear programming to gain further efficiency. The proposed method has the advantages that it can handle arbitrary structures and larger-scale problems. Experimental results on part-of-speech tagging and statistical machine translation tasks are reported, demonstrating the competitiveness of our approach.