  Most of the unsupervised dependency parsers are based on first-order
probabilistic generative models that only consider local parent-child
information. Inspired by second-order supervised dependency parsing, we
proposed a second-order extension of unsupervised neural dependency models that
incorporate grandparent-child or sibling information. We also propose a novel
design of the neural parameterization and optimization methods of the
dependency models. In second-order models, the number of grammar rules grows
cubically with the increase of vocabulary size, making it difficult to train
lexicalized models that may contain thousands of words. To circumvent this
problem while still benefiting from both second-order parsing and
lexicalization, we use the agreement-based learning framework to jointly train
a second-order unlexicalized model and a first-order lexicalized model.
Experiments on multiple datasets show the effectiveness of our second-order
models compared with recent state-of-the-art methods. Our joint model achieves
a 10% improvement over the previous state-of-the-art parser on the full WSJ
test set
