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<Paper uid="H89-2020">
  <Title>A Simple Statistical Class Grammar for Measuring Speech Recognition Performance</Title>
  <Section position="3" start_page="0" end_page="147" type="intro">
    <SectionTitle>
2 DESCRIPTION
</SectionTitle>
    <Paragraph position="0"> The grammar that we developed is a statistical first-order class grammar m which the probability of a word (W1) being followed by another word (W2) is given by:</Paragraph>
    <Paragraph position="2"> Where C1 is each of the classes to which WI belongs, and C2 is each of the classes to which W2 be- null longs. Since each of W I and W2 may belong to multiple classes, the summation is over all possible paths fxom W1 to W2. This is represented graphically below:</Paragraph>
    <Paragraph position="4"> Note that, in the diagram, the silence at the beginning of a sentence (&amp;quot;start silence&amp;quot;) and the silence at the end of a sentence (&amp;quot;end silence&amp;quot;) are simply special cases of WI and |V2, respectively, where each is in a separate class. The &amp;quot;'class node w/silence loop&amp;quot; indicates that a silence may be inserted between each word.</Paragraph>
    <Paragraph position="5"> In our work to date, we have made two simplifying assumptions. The conditional probability P(CIiWI) is approximated by: Nwlgcl -~ for Wl in CI</Paragraph>
    <Paragraph position="7"> Where Nw~c~ is the number of classes of which word W1 is a member. (For example, if a word is a member of two classes, PfCIlWI) will be 0.5 for each of those classes and 0.0 for all other classes.) A similar approximation is made for P(W2--C2), where:</Paragraph>
    <Paragraph position="9"> Where NwzEc2 is the number of words in class C2.</Paragraph>
    <Paragraph position="10"> The probabilities P(CIIWD and PfW2!C2) are fixed and not changed during the training of the grammar.</Paragraph>
    <Paragraph position="11"> With this simplification, the only term that must be estimated during the training of the grammar is P(C2!CI), the class-to-class transition probabilities.</Paragraph>
  </Section>
class="xml-element"></Paper>