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<Paper uid="W06-3606">
  <Title>Practical Markov Logic Containing First-Order Quantifiers with Application to Identity Uncertainty</Title>
  <Section position="6" start_page="46" end_page="47" type="concl">
    <SectionTitle>
5 Conclusions and Future Work
</SectionTitle>
    <Paragraph position="0"> We have presented an algorithm that enables practical inference in MLNs containing first-order existential and universal quantifiers, and have demonstrated the advantages of this approach on two real-world datasets. Future work will investigate efficient ways to improve the approximations made during inference, for example by reducing its greediness by revising the MAP estimates made at previous iterations.</Paragraph>
    <Paragraph position="1"> Although the optimal number of objects is chosen implicitly by the inference algorithm, there may be reasons to explicitly model this number. For example, if there exist global features of the data that suggest there are many objects, then the inference algorithm should be less inclined to merge constants.</Paragraph>
    <Paragraph position="2"> Additionally, the data may exhibit &amp;quot;preferential attachment&amp;quot; such that the probability of a constant being added to an existing object is proportional to the number of constants that refer to that object.</Paragraph>
    <Paragraph position="3"> Future work will examine the feasibility of adding aggregate query predicates to represent these values.</Paragraph>
    <Paragraph position="4"> More subtly, one may also want to directly model the size of the object population. For example, given a database of authors, we may want to estimate not only how many distinct authors exist in the database, but also how many distinct authors exist outside of the database, as discussed in Milch et al. (2005).</Paragraph>
    <Paragraph position="5"> Discriminatively-trained models cannot easily reason about objects for which they have no observations; so a generative/discriminative hybrid model may be required to properly estimate this value.</Paragraph>
    <Paragraph position="6"> Finally, while the inference algorithm we describe is evaluated only on the object uncertainty task, we would like to extend it to perform inference over arbitrary query predicates.</Paragraph>
  </Section>
class="xml-element"></Paper>