Unsupervised models of dependency parsing typically require large amounts of clean, unlabeled data plus gold-standard part-of-speech tags. Adding indirect supervision (e.g. language universals and rules) can help, but we show that obtaining small amounts of direct supervision - here, partial dependency annotations - provides a strong balance between zero and full supervision. We adapt the unsupervised ConvexMST dependency parser to learn from partial dependencies expressed in the Graph Fragment Language. With less than 24 hours of total annotation, we obtain 7% and 17% absolute improvement in unlabeled dependency scores for English and Spanish, respectively, compared to the same parser using only universal grammar constraints.
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