  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.
