As an approach to syntax based statistical machine translation (SMT), Probabilistic Synchronous Dependency Insertion Grammars (PSDIG), introduced in (Ding and Palmer, 2005), are a version of synchronous grammars defined on dependency trees. In this paper we discuss better learning and decoding algorithms for a PSDIG MT system. We introduce two new grammar learners: (1) an exhaustive learner combining different heuristics, (2) an n-gram based grammar learner. Combining the grammar rules learned from the two learners improved the performance. We introduce a better decoding algorithm which incorporates a tri-gram language model. According to the Bleu metric, the PSDIG MT system performance is significantly better than IBM Model 4, while on par with the state-of-the-art phrase based system Pharaoh (Koehn, 2004). The improved integration of syntax on both source and target languages opens door to more sophisticated SMT processes.

Structural divergence presents a challenge to the use of syntax in statistical machine translation. We address this problem with a new algorithm for alignment of loosely matched non-isomorphic dependency trees. The algorithm selectively relaxes the constraints of the two tree structures while keeping computational complexity polynomial in the length of the sentences. Experimentation with a large Chinese-English corpus shows an improvement in alignment results over the unstructured models of (Brown et al., 1993).