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<Paper uid="P02-1036">
  <Title>Dynamic programming for parsing and estimation of stochastic uni cation-based grammars</Title>
  <Section position="7" start_page="0" end_page="0" type="concl">
    <SectionTitle>
5 Conclusion
</SectionTitle>
    <Paragraph position="0"> This paper shows how to apply dynamic programming methods developed for graphical models to SUBGs to nd the most probable parse and to obtain the statistics needed for estimation directly from Maxwell and Kaplan packed parse representations.</Paragraph>
    <Paragraph position="1"> i.e., without expanding these into individual parses.</Paragraph>
    <Paragraph position="2"> The algorithm rests on the observation that so long as features are local to the parse fragments used in the packed representations, the statistics required for parsing and estimation are the kinds of quantities that dynamic programming algorithms for graphical models can perform. Since neither Maxwell and Kaplan's packed parsing algorithm nor the procedures described here depend on the details of the underlying linguistic theory, the approach should apply to virtually any kind of underlying grammar.</Paragraph>
    <Paragraph position="3"> Obviously, an empirical evaluation of the algorithms described here would be extremely useful.</Paragraph>
    <Paragraph position="4"> The algorithms described here are exact, but because we are working with uni cation grammars and apparently arbitrary graphical models we cannot polynomially bound their computational complexity. However, it seems reasonable to expect that if the linguistic dependencies in a sentence typically factorize into largely non-interacting cliques then the dynamic programming methods may offer dramatic computational savings compared to current methods that enumerate all possible parses.</Paragraph>
    <Paragraph position="5"> It might be interesting to compare these dynamic programming algorithms with a standard uni cation-based parser using a best- rst search heuristic. (To our knowledge such an approach has not yet been explored, but it seems straightforward: the gure of merit could simply be the sum of the weights of the properties of each partial parse's fragments). Because such parsers prune the search space they cannot guarantee correct results, unlike the algorithms proposed here. Such a best- rst parser might be accurate when parsing with a trained grammar, but its results may be poor at the beginning of parameter weight estimation when the parameter weight estimates are themselves inaccurate.</Paragraph>
    <Paragraph position="6"> Finally, it would be extremely interesting to compare these dynamic programming algorithms to the ones described by Miyao and Tsujii (2002). It seems that the Maxwell and Kaplan packed representation may permit more compact representations than the disjunctive representations used by Miyao et al., but this does not imply that the algorithms proposed here are more ef cient. Further theoretical and empirical investigation is required.</Paragraph>
  </Section>
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