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We apply machine learning to the Linear Ordering Problem in order to learn sentence-specific reordering models for machine translation. We demonstrate that even when these models are used as a mere preprocessing step for German-English translation, they significantly outperform Moses' integrated lexicalized reordering model.  Our models are trained on automatically aligned bitext. Their form is simple but novel. They assess, based on features of the input sentence, how strongly each pair of input word tokens wi, wj would like to reverse their relative order. Combining all these pairwise preferences to find the best global reordering is NP-hard. However, we present a non-trivial O(n3) algorithm, based on chart parsing, that at least finds the best reordering within a certain exponentially large neighborhood. We show how to iterate this reordering process within a local search algorithm, which we use in training.

Learning linear ordering problems for better translation