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<Paper uid="C04-1030">
  <Title>Reordering Constraints for Phrase-Based Statistical Machine Translation</Title>
  <Section position="2" start_page="0" end_page="0" type="intro">
    <SectionTitle>
1 Introduction
</SectionTitle>
    <Paragraph position="0"> In statistical machine translation, we are given a source language ('French') sentence fJ1 = f1 :::fj :::fJ, which is to be translated into a target language ('English') sentence eI1 = e1 :::ei :::eI: Among all possible target language sentences, we will choose the sentence with the highest probability:  This decomposition into two knowledge sources is known as the source-channel approach to statistical machine translation (Brown et al., 1990). It allows an independent modeling of target language model Pr(eI1) and translation model Pr(fJ1 jeI1). The target language model describes the well-formedness of the target language sentence. The translation model links the source language sentence to the target language sentence. It can be further decomposed into alignment and lexicon model. The argmax operation denotes the search problem, i.e. the generation of the output sentence in the target language. We have to maximize over all possible target language sentences.</Paragraph>
    <Paragraph position="1"> An alternative to the classical source-channel approach is the direct modeling of the posterior probability Pr(eI1jfJ1 ). Using a log-linear model (Och and Ney, 2002), we obtain:</Paragraph>
    <Paragraph position="3"> Here, Z(fJ1 ) denotes the appropriate normalization constant. As adecision rule, weobtain:</Paragraph>
    <Paragraph position="5"> This approach is a generalization of the source-channel approach. It has the advantage that additional models or feature functions can be easily integrated into the over-all system. The model scaling factors ,M1 are trained according to the maximum entropy principle, e.g. using the GIS algorithm. Alternatively, one can train them with respect to the final translation quality measured by some error criterion (Och, 2003).</Paragraph>
    <Paragraph position="6"> In this paper, we will investigate the re-ordering problem for phrase-based translation approaches. As the word order in source and target language may differ, the search algorithm has to allow certain reorderings. If arbitrary reorderings are allowed, the search problem is NP-hard (Knight, 1999). To obtain an efficient search algorithm, we can either restrict the possible reorderings or we have to use an approximation algorithm. Note that in the latter case we cannot guarantee to find an optimal solution.</Paragraph>
    <Paragraph position="7"> The remaining part of this work is structured as follows: in the next section, we will review the baseline translation system, namely the alignment template approach. Afterward, we will describe different reordering constraints. We will begin with the IBM constraints for phrase-based translation. Then, we will describe constraints based on inversion transduction grammars (ITG). In the following, we will call these the ITG constraints. In Section 4, we will present results for two Japanese-English translation tasks.</Paragraph>
  </Section>
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