This article is a very difficult one. As a matter of fact it needs mathematical literacy in order to understand it. What I understand from the article is the fact that writer says there are various ways to create a model for equivalence in translation at the same time there are many ways to estimate translation model. The mathematics of statistical machine translation is one kind of mathematics for one kind of statistical translation. In this article, the writer proposed and evaluated new kinds of translation models. It is done via distinguishing parallel texts from parallel data. To this end, first, most words translate to only one word. Second, bi text correspondence is typically partial. Many words in each text have no clear equivalent in the other text. In fact, the writer of this article introduces methods for biasing statistical translation models to reflect these properties. At the end of the article evaluation with respect to independent human judgment approved that translation models biased in this fashion are significantly more accurate than a base line knowledge free model. Although the methodology and explanation are difficult to understand, the result of the study is understandable.
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