Marcus and Wong, EMNLP 2002

Model

The phrase-to-phrase alignment model presented in this work is built upon the work in (Marcus and Wong, 2002). In this work, words are clustered into phrases by a generative process, which constructs an ordered set of phrases $t_{1:m}$ in the target language, an ordered set of phrases $s_{1:n}$ in the source language and the alignments between phrases $a=\{(j,k)\}$, which indicates that the phrase pair with the target $t_{j}$ and $s_{k}$. The process is composed by 2 steps:

• First, the number of components $l$ is chosen and each of $l$ phrase pairs are generated independently.
• Then, a ordering for the phrases in the source phrases is chosen, and all the source and target phrases are aligned one to one.

The choice of $l$ is parametrized using a geometric distribution $P_{G}$, with the stop parameter $p_{\$}$:

$P(l)=P_{G}(l;p_{\$})=p_{\$}\times (1-p_{\$})^{l-1}$

Phrase pairs are drawn from an unknown multinomial distribution $\theta _{J}$.

A simple position based distortion model is used, where:

$P(a|[t,s])\propto \prod _{a_{i}\in a}\delta (a_{i})$

$P(a_{i}=(j,k))=b^{|pos(t_{j})-pos(s_{k})\times s|}$

Finally, the joint probability model for aligning sentences consisting of $l$ phrase pairs is given by:

$P([t,s],a)=P_{G}(l;p_{\$})P(a|[t,s])\prod _{[t,s]}\theta _{J}([t,s])$

In the experiments paramters $p_{\$}$ and $b$ were set to 0.1 and 0.85, respectively.