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<Paper uid="C00-2109">
  <Title>Backward Beam Search Algorithm for Dependency Analysis of Japanese</Title>
  <Section position="4" start_page="754" end_page="755" type="metho">
    <SectionTitle>
2 Statistic framework
</SectionTitle>
    <Paragraph position="0"> We. coin|lined tile backward beam search strategy with a statistical dependency analysis. 'rile det~fil of our statistic framework is described ill (Uehimoto et al., 1999). There have been a lot of prol)OS~fls for statistical analysis, in ninny languages, in particular in English and Japanese (Magerman, 1995) (Sekine and Grishman, 1995) (Collins, 1997) (I/atnal)arkhi, 1997) (K.Shirai et.al, 1998) (Fujio and Matsnlnoto, 1998) (Itaruno ct.al, 1997)(Ehara, 1998). One of the most advance(t systems in English is l)roposed 1)y I{atnaparkhi. It, uses the Maximum Entropy (ME) model and both of the accuracy and the speed of the system arc among the best ret)ortcd to date. Our system uses the ME model, too. in the ME model, we define a set el! \]2~,atlll'eS which arc thought to l)e uscflfl in del)ealden(:y analysis, and it: learns the weights of the R~atures fl'om training data. Our t~ntttres in(:lude part-of-st)eech, inflections, lexical items, the existence of a contain or bra(:ket 1)etween the segments, and the distmme between the segments. Also, confl)inations of those features are used as additional fe, atures. The system eal(:ulates the probabilities of dependencies based on the model, which is trained using a training corpus. The probability of an entire sentence is derived from the 1)roduct of tile probal)ilities of all the dependencies in the sentence. We choose the analysis with the highest probafl)ility to be the analysis of the sentence. Although the accuracy of the analyzer is not the main issue of the t)al)er, as any types of models which use de1)endency 1)rol)al)ilities can be iml)lelnented by our method, the 1)ertbrmance ret)orted in (Uchilnoto et al., 1999) is one of the best results reported by statistic~flly based systems.</Paragraph>
  </Section>
  <Section position="5" start_page="755" end_page="756" type="metho">
    <SectionTitle>
3 Algorithm
</SectionTitle>
    <Paragraph position="0"> In this section, the analysis algorithm will be described. First the algorithm will be illustrated using an example, then the algorithm will be formally described. The main characteristics of the algorithm are the backward analysis and the beam search. The sentence &amp;quot;KARE-HA FUTATABI PAI-W\[I TSUKURI, KANOJ0-NI 0KUTTA. (He made a pie again and presented it to her)&amp;quot; is used as an input. We assume the POS tagging and segmentation analysis have been done correctly before starting the process. The border of each segment is shown by &amp;quot;1&amp;quot;. In the figures, the head of the dependency for each segment is represented by the segment number shown at the top of each  1. Analyze np to the second segment from the end  The last segment has no dependency, so we don't have to analyze it. The second segment fl'om the end always depends on the last segment. So the result up to the secend segment from the end looks like the following.</Paragraph>
    <Paragraph position="1"> &lt;Up to the second segment from the end&gt;</Paragraph>
    <Paragraph position="3"> .................................................................</Paragraph>
    <Paragraph position="4"> . The third segment from the end This segment (&amp;quot;TSUKURI,&amp;quot; ) has two dependency candidates. One is the 5th segment (&amp;quot;KANOJ0-NI&amp;quot;) and the other is the 6th segment (&amp;quot;0KUTTA&amp;quot;). Now, we use the probabilities calculated using the ME model in order to assign probabilities to the two candidates (Candl and Cand2 in the following figure). Let's assume the probabilities 0.1 and 0.9 respectively as an example. At the tail of each analysis, the total probability (the product of the probabilities of all dependencies) is shown. The candidates are sorted by the total probability.</Paragraph>
    <Paragraph position="5"> .</Paragraph>
    <Paragraph position="6"> &lt;Up to the third segment from the end&gt;</Paragraph>
    <Paragraph position="8"> .................................................................</Paragraph>
    <Paragraph position="9"> The tburth segment from the end For each of the two candidates created at the previous stage, the dependencies of the fburth segment from the end (&amp;quot;PAI-W0&amp;quot;) will be analyzed. For Candl, the segment can't have a dependency to the fifth segment (&amp;quot;KANOJ0-1gI&amp;quot;), because of the non-crossing assmnption. So the probabilities of the dependencies only to the fourth (Candi-1) and the sixth (Candi-2) segments are calculated. In the example, these probabilities are assmned to be 0.6 and 0.4.</Paragraph>
    <Paragraph position="10"> A similar analysis is conducted for Cand2 (here probabilities are assumed to be 0.5,  ................................................................. As tile analysis proceeds, a large number (almost L!) of candidates will he created.</Paragraph>
    <Paragraph position="11"> However, by linfiting the number of candidates at each stage, the total nmnber of candidates can be reduced. This is the beam search, one of the characteristics of the algorithm. By observing the analyses in the example, we can e~sily imagine that this beam search may not cause a serious problem in performance, because the candidates with low probabilities may be incorrect anyway. For instance, when we set the beam search width = 3, then Canal2-2 and Cand2-3 in the figure will be discarded at this stage, and hence won't be used in the following analyses. The relationship of the beam search width and the accuracy ohserved in our experiments will be reported in the next section.</Paragraph>
    <Paragraph position="12">  . Up to the, first segment The analyses are conducted in the, same way up to the first segment. For example, the result of tile analysis tbr the entire selltence will be shown below. (Appropriate, probabilities are used.) 4.2 Beam search width and accuracy In this subsection, the relationship between the beam width and the accuracy is discussed. In principle, the wider the beam search width, the more analyses can be retained and the better the accuracy cml be expected. However, the re.................................................................. sult is somewhat different froan tile expectation.  Now, the formal algorithm is described inductiveJy in Figure 3. The order of the analysis is quadratic ill the length of the sentence.</Paragraph>
  </Section>
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