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<Paper uid="W99-0631">
  <Title>An Iterative Approach to Estimating Frequencies over a Semantic Hierarchy</Title>
  <Section position="8" start_page="262" end_page="263" type="evalu">
    <SectionTitle>
6 Experimental Results
</SectionTitle>
    <Paragraph position="0"> In order to evaluate the re-estimation procedure, we took triples from approximately two million words of parsed text from the SLow counts tend to occur in the table when the test is being applied to a set of concepts near the foot of the hierarchy. A further extension of this work will be to use Fisher's exact test for the tables with particularly low counts.</Paragraph>
    <Paragraph position="1"> BNC corpus using the shallow parser developed by Briscoe and Carroll (1997). For this work we only considered triples for which r = obj. Table 2 shows some examples of how the log-likelihood X 2 test chooses top(c, v, r) for various v 6 V and c 6 C. 9 In giving the list of hypernyms the selected concept top(c, v, obj) is shown in upper case.</Paragraph>
    <Paragraph position="2"> Table 3 shows how frequency estimates change, during the re-estimation process, for various v E ~, c E C, and r = obj. The figures in Table 3 show that the estimates appear to be converging after around 10 iterations. The first column gives the frequency estimates using the technique of splitting the count equally among alternative senses of a noun appearing in the data. The figures for eat and drink suggest that these initial estimates can be greatly underestimated (and also overestimated for cases where the argument strongly violates the selectional preferences of the verb, such as eat &lt;location&gt;). The final column gives an upper bound on the re-estimated frequencies. It shows how many nouns in the data, in the object position of the given verb, that could possibly be denoting one of the concepts in ~, for each v and ~ in the table. For example, 95 is the number of times a noun which could possibly 9Notice that &lt; hotdog &gt; is classified at the &lt;nutriment&gt; level rather than &lt;food&gt;. This is presumably due to the fact that beverage is classed as a food, making the set of concepts &lt;food&gt; heterogenous with respect to the object position of eat.</Paragraph>
    <Paragraph position="4"> be denoting a concept dominated by (food&gt; appeared in the object position of eat. Since eat selects so strongly for its object, we would expect freq(&lt;food&gt;,eat, obj) (i.e., the true figure) to be close to 95. Similarly, since drink selects so strongly for its object, we would expect freq(&lt; beverage &gt;,drink, obj) to be close to 26. We would also expect freq(&lt;location&gt;,eat, obj) to be close to 0.</Paragraph>
    <Paragraph position="5"> As can be seen from Table 3, our estimates converge quite closely to these values.</Paragraph>
    <Paragraph position="6"> It is noticeable that the frequency counts for weakly selecting verbs do not change as much as for strongly selecting verbs. Thus, the benefit we achieve compared to the standard approach of distributing counts evenly is reduced in these cases. In order to investigate the extent to which our technique may be helping, for each triple in the data we calculated how the distribution of the count changed due to our re-estimation technique.</Paragraph>
    <Paragraph position="7"> We estimated the extent to which the distribution had changed by calculating the percentage increase in the count for the most favoured sense after 10 iterations. Table 4 shows the results we obtained. The proportions given in the second column are of the triples in the data containing nouns with more than one sense. 1deg We can see from the 1deg17% of the data involved nouns with only one sense in W0rdNet.</Paragraph>
    <Paragraph position="8"> table that for 43% of the triples our technique is having little effect, but for 23% the count is at least doubled.</Paragraph>
  </Section>
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