  Prior work on cross-lingual dependency parsing often focuses on capturing the
commonalities between source and target languages and overlooks the potential
of leveraging linguistic properties of the languages to facilitate the
transfer. In this paper, we show that weak supervisions of linguistic knowledge
for the target languages can improve a cross-lingual graph-based dependency
parser substantially. Specifically, we explore several types of corpus
linguistic statistics and compile them into corpus-wise constraints to guide
the inference process during the test time. We adapt two techniques, Lagrangian
relaxation and posterior regularization, to conduct inference with
corpus-statistics constraints. Experiments show that the Lagrangian relaxation
and posterior regularization inference improve the performances on 15 and 17
out of 19 target languages, respectively. The improvements are especially
significant for target languages that have different word order features from
the source language.
