  We introduce two first-order graph-based dependency parsers achieving a new
state of the art. The first is a consensus parser built from an ensemble of
independently trained greedy LSTM transition-based parsers with different
random initializations. We cast this approach as minimum Bayes risk decoding
(under the Hamming cost) and argue that weaker consensus within the ensemble is
a useful signal of difficulty or ambiguity. The second parser is a
"distillation" of the ensemble into a single model. We train the distillation
parser using a structured hinge loss objective with a novel cost that
incorporates ensemble uncertainty estimates for each possible attachment,
thereby avoiding the intractable cross-entropy computations required by
applying standard distillation objectives to problems with structured outputs.
The first-order distillation parser matches or surpasses the state of the art
on English, Chinese, and German.
