Discriminative training and variational decoding in machine translation via novel algorithms for weighted hypergraphs

A hypergraph or "packed forest" is a compact data structure that uses structure-sharing to represent exponentially many trees in polynomial space. A probabilistic/weighted hypergraph also defines a probability (or other weight) for each tree, and can be used to represent the hypothesis space considered (for a given input) by a monolingual parser or a tree-based translation system (e.g., tree to string, string to tree, tree to tree, or string to string with latent tree structures). Given a weighted/probabilistic hypergraph, we might ask three questions. What atomic operations can we perform on the weighted hypergraph? How do we set the weights in the hypergraph? Which particular translation (among the possible translations encoded in a hypergraph) should we present to an end user? These correspond to three fundamental problems: inference, training, and decoding, for which this dissertation will present novel techniques. The atomic inference operations we may want to perform include finding one-best, k-best, or expectations over the hypergraph. To perform each operation, we may implement a dedicated dynamic programming algorithm. However, a more general framework to specify these algorithms is semiring-weighted logic programming. Within this framework, we first extend the expectation semiring, which is originally proposed for a finite state automaton, to a hypergraph. We then propose a novel second-order expectation semiring. These semirings can be used to compute a large number of expectations (e.g., entropy and its gradient) over the exponentially many trees presented in a hypergraph. The weights used in a hypergraph are usually learnt by a discriminative training method. One common drawback of such method is that it relies on the existence of high-quality supervised data (i.e., bilingual data), which may be expensive to obtain. We present two unsupervised discriminative training methods: minimum imputed-risk training, and contrastive language model estimation, both can exploit monolingual English data to perform discriminative training. In minimum imputed-risk training, we first use a reverse translation model to impute the missing inputs, and then train a discriminative forward model by minimizing the expected loss of the forward translations of the missing inputs. In contrast, the contrastive language model estimation does not use a reverse system. It first extracts a confusion grammar, then generates many alternative sentences (i.e., a contrastive set) for each English sentence using the confusion grammar, and finally trains a discriminative language model on the contrastive sets such that the model will prefer the original English sentences (over the sentences in the contrastive sets). During decoding, we are interested in finding a translation that has a maximum posterior probability (i.e., MAP decoding). However, this is intractable due to spurious ambiguity, a situation where the probability of a translation string is split among many distinct derivations (e.g., trees or segmentations). Therefore, most systems use a simple Viterbi decoding that approximates the string probability with its most probable derivation's probability. Instead, we develop a variational approximation, which considers all the derivations but still allows tractable decoding. Our particular variational distributions are parameterized as n-gram models. We also analytically show that interpolating these n-gram models for different n is similar to lattice-based minimum-risk decoding for BLEU. Experiments show that our approach improves the state of the art. All the above methods have been implemented in an open-source machine translation toolkit Joshua. In this dissertation, the methods have mainly been applied to a machine translation task, butwe expect that they will also find applications in other areas of natural language processing (e.g., parsing and speech recognition).