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<Paper uid="E99-1026">
  <Title>Japanese Dependency Structure Analysis Based on Maximum Entropy Models</Title>
  <Section position="3" start_page="196" end_page="196" type="metho">
    <SectionTitle>
2 The Probability Model
</SectionTitle>
    <Paragraph position="0"> Given a tokenization of a test corpus, the problem of dependency structure analysis in Japanese can be reduced to the problem of assigning one of two tags to each relationship which consists of two bunsetsus. A relationship could be tagged as &amp;quot;0&amp;quot; or &amp;quot;1&amp;quot; to indicate whether or not there is a dependency between the bunsetsus, respectively.</Paragraph>
    <Paragraph position="1"> The two tags form the space of &amp;quot;futures&amp;quot; for a maximum entropy formulation of our dependency problem between bunsetsus. A maximum entropy solution to this, or any other similar problem allows the computation of P(f\[h) for any f from the space of possible futures, F, for every h from the space of possible histories, H. A &amp;quot;history&amp;quot; in maximum entropy is all of the conditioning data which enables you to make a decision among the space of futures. In the dependency problem, we could reformulate this in terms of finding the probability of f associated with the relationship at index t in the test corpus as:</Paragraph>
    <Paragraph position="3"> from the test corpus related to relationship t) The computation of P(f\]h) in M.E. is dependent on a set of '`features&amp;quot; which, hopefully, are helpful in making a prediction about the future. Like most current M.E. modeling efforts in computational linguistics, we restrict ourselves to features which are binary functions of the history and aAssumption (4) has not been discussed very much, but our investigation with humans showed that it is true in more than 90% of cases.</Paragraph>
    <Paragraph position="4"> future. For instance, one of our features is</Paragraph>
    <Paragraph position="6"> Here &amp;quot;has(h,z)&amp;quot; is a binary function which returns true if the history h has an attribute x. We focus on attributes on a bunsetsu itself and those between bunsetsus. Section 3 will mention these attributes.</Paragraph>
    <Paragraph position="7"> Given a set of features and some training data, the maximum entropy estimation process produces a model in which every feature gi has associated with it a parameter ai. This allows us to compute the conditional probability as follows (Berger et al., 1996):</Paragraph>
    <Paragraph position="9"> The maximum entropy estimation technique guarantees that for every feature gi, the expected value of gi according to the M.E. model will equal the empirical expectation of gi in the training corpus. In other words:</Paragraph>
    <Paragraph position="11"> Here /3 is an empirical probability and PME is the probability assigned by the M.E. model.</Paragraph>
    <Paragraph position="12"> We assume that dependencies in a sentence are independent of each other and the overall dependencies in a sentence can be determined based on the product of probability of all dependencies in the sentence.</Paragraph>
    <Paragraph position="13"> if has(h, x) = ture,</Paragraph>
    <Paragraph position="15"/>
  </Section>
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