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# Large-Margin Structured Prediction via Linear Programming

*Proceedings of the Twelfth International Conference on Artificial Intelligence and Statistics*, PMLR 5:599-606, 2009.

#### Abstract

This paper presents a novel learning algorithm for structured classification problems, where the task is to predict multiple and interacting labels (multilabel) for an input object. The maximum margin separation between the correct multilabels and the 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 the column generation and the extragradient method for linear programming to gain further efficiency. Compared to previous works on large-margin structured prediction, this framework has advantages in handling arbitrary structures and larger-scale problems. Experimental results on part-of-speech tagging and statistical machine translation tasks are reported, demonstrating the competitiveness of the proposed approach.