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<Paper uid="W06-2918">
  <Title>Using Gazetteers in Discriminative Information Extraction</Title>
  <Section position="4" start_page="133" end_page="133" type="intro">
    <SectionTitle>
2 Conditional Random Fields
</SectionTitle>
    <Paragraph position="0"> A linear chain conditional random eld (CRF) (Lafferty et al., 2001) de nes the conditional probability of a label sequence s given an observed sequence o via:</Paragraph>
    <Paragraph position="2"> where T is the length of both sequences, lk are parameters of the model and Za0 oa2 is a partition function that ensures that (1) represents a probability distribution. The functions fk are feature functions representing the occurrence of different events in the sequences s and o.</Paragraph>
    <Paragraph position="3"> The parameters lk can be estimated by maximising the conditional log-likelihood of a set of labelled training sequences. At the maximum likelihood solution the model satis es a set of feature constraints, whereby the expected count of each feature under the model is equal to its empirical count on the training data:</Paragraph>
    <Paragraph position="5"> In general this cannot be solved for the lk in closed form, so numerical optimisation must be used. For our experiments we use the limited memory variable metric (LMVM) (Sha and Pereira, 2003) routine, which has become the standard algorithm for CRF training with a likelihood-based objective function.</Paragraph>
    <Paragraph position="6"> To avoid over tting, a prior distribution over the model parameters is typically used. A common example of this is the Gaussian prior. Use of a prior involves adding extra terms to the objective and its derivative. In the case of a Gaussian prior, these additional terms involve the mean and variance of the distribution.</Paragraph>
  </Section>
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