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<Paper uid="P94-1011">
  <Title>PRECISE N-GRAM PROBABILITIES FROM STOCHASTIC CONTEXT-FREE GRAMMARS</Title>
  <Section position="10" start_page="77" end_page="77" type="concl">
    <SectionTitle>
CONCLUSIONS
</SectionTitle>
    <Paragraph position="0"> We. have described an algorithm to compute in closed form the distribution of n-grams for a probabilistic language given by a stochastic context-free grammar. Our method is based on computing substring expectations, which can be expressed as systems of linear equations derived from the grammar. The algorithm was used successfully and found to be practical in dealing with context-free grammars and bigram models for a medium-scale speech recognition task, where it helped to improve bigram estimates obtained from relatively small amounts of data.</Paragraph>
    <Paragraph position="1"> Deriving n-gram probabilities from more sophisticated language models appears to be a generally useful technique which can both improve upon direct estimation of n-grams, and allow available higher-level linguistic knowledge to be effectively integrated into the speech decoding task.</Paragraph>
  </Section>
class="xml-element"></Paper>