  This paper presents generalized probabilistic models for high-order
projective dependency parsing and an algorithmic framework for learning these
statistical models involving dependency trees. Partition functions and
marginals for high-order dependency trees can be computed efficiently, by
adapting our algorithms which extend the inside-outside algorithm to
higher-order cases. To show the effectiveness of our algorithms, we perform
experiments on three languages---English, Chinese and Czech, using maximum
conditional likelihood estimation for model training and L-BFGS for parameter
estimation. Our methods achieve competitive performance for English, and
outperform all previously reported dependency parsers for Chinese and Czech.
