Title: Exact and Approximate Methods for Machine Translation Decoding
Description: Statistical methods have been the major force driving the advance of machine translation in recent years. Complex models are designed to improve translation performance, but the added complexity also makes decoding more challenging. In this thesis, we focus on designing exact and approximate algorithms for machine translation decoding. More specifically, we will discuss the decoding problems for phrase-based translation models and bidirectional word alignment. The techniques explored in this thesis are Lagrangian relaxation and local search. Lagrangian relaxation based algorithms give us exact methods that have formal guarantees while being efficient in practice. We study extensions to Lagrangian relaxation that improve the convergence rate on machine translation decoding problems. The extensions include a tightening technique that adds constraints incrementally, optimality-preserving pruning to manage the search space size and utilizing the bounding properties of Lagrangian relaxation to develop an exact beam search algorithm.

In addition to having the potential to improve translation accuracy, exact decoding deepens our understanding of the model that we are using, since it separates model errors from optimization errors. This leads to the question of designing models that improve the translation quality. We design a syntactic phrase-based model that incorporates a dependency language model to evaluate the fluency level of the target language. By employing local search, an approximate method, to decode this richer model, we discuss the trade-off between the complexity of a model and the decoding efficiency with the model.