Vogal et al, COLING 1996

Citation

Vogel, S., Ney, H., & Tillmann, C. (1996). Hmm-based word alignment in statistical translation. In Proceedings of the 16th conference on Computational linguistics - Volume 2, COLING ’96, pp. 836–841, Stroudsburg, PA, USA. Association for Computational Linguistics.

Online version

ACM

Summary

Word Alignments map the word correspondence between two parallel sentences in different languages.

This work extends IBM models 1 and 2, which models lexical translation probabilities and absolute distortion probabilities, by also modeling relative distortion.

The relative distortion is modeled by applying a first-order HMM, where each alignment probabilities are dependent on the distortion of the previous alignment.

Previous work

IBM Model 1<ref>Brown, P. F., Pietra, V. J. D., Pietra, S. A. D., & Mercer, R. L. (1993). The mathematics of statistical machine translation: parameter estimation. Comput. Linguist., 19, 263–311.</ref> defines the probability of a sentence $s_{1}^{J}$, with length $J$, being translated to a sentence $t_{1}^{I}$, with length $I$, with the alignment $a_{1}^{J}$ as:

$Pr(t,a|s)={\frac {\epsilon }{(J+1)^{I}}}\prod _{j=1}^{J}{tr(t_{j}|s_{a(j)})}$

Where the alignment $a_{1}^{J}$ is a function that maps each word $t_{j}$ to a word $s_{i}$, by their indexes. These alignments can be viewed as an object for indicating the corresponding words in a parallel text. We can see that the sentence translation probability $Pr(t,s)$, is decomposed into the product of the lexical translation probabilities $tr(t_{j}|s_{a(j)})$ of each word in the target $t_{1},...,t_{J}$ with the word that it is aligned to in the source $s_{a(j)}$. Additionally, target words that are not aligned with any source word are aligned with the null token, with the a lexical translation probability given by $tr(t_{j}|null)$. These are referred as null insertions. The normalizing factor ${\frac {\epsilon }{(I+1)^{J}}}$ ensures that $Pr(t,a|s)$ is a probability and is normalized over all possible alignments $a$ and all possible translations $t$.

Algorithm

While IBM Model 2 attempts to model the absolute distortion of words in sentence pairs $Pr_{a}(i|j,J,I)$, alignments have a strong tendency to maintain the local neighborhood after translation.