The Mathematics of Statistical Machine Translation: Parameter Estimation

We describe a series o,f five statistical models o,f the translation process and give algorithms,for estimating the parameters o,f these models given a set o,f pairs o,f sentences that are translations o,f one another. We define a concept o,f word-by-word alignment between such pairs o,f sentences. For any given pair of such sentences each o,f our models assigns a probability to each of the possible word-by-word alignments. We give an algorithm for seeking the most probable o,f these alignments. Although the algorithm is suboptimal, the alignment thus obtained accounts well for the word-by-word relationships in the pair o,f sentences. We have a great deal o,f data in French and English from the proceedings o,f the Canadian Parliament. Accordingly, we have restricted our work to these two languages; but we,feel that because our algorithms have minimal linguistic content they would work well on other pairs o,f languages. We also ,feel, again because of the minimal linguistic content o,f our algorithms, that it is reasonable to argue that word-by-word alignments are inherent in any sufficiently large bilingual corpus.