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<Paper uid="W06-3606">
  <Title>Practical Markov Logic Containing First-Order Quantifiers with Application to Identity Uncertainty</Title>
  <Section position="3" start_page="41" end_page="41" type="relat">
    <SectionTitle>
2 Related Work
</SectionTitle>
    <Paragraph position="0"> MLNs were designed to subsume various previously proposed statistical relational models. Probabilistic relational models (Friedman et al., 1999) combine descriptive logic with directed graphical models, but are restricted to acyclic graphs. Relational Markov networks (Taskar et al., 2002) use SQL queries to specify the structure of undirected graphical models. Since first-order logic subsumes SQL, MLNs can be viewed as more expressive than relational Markov networks, although existing applications of MLNs have not fully utilized this increased expressivity. Other approaches combining logic programming and log-linear models include stochastic logic programs (Cussens, 2003) and MACCENT(Dehaspe, 1997), although MLNs can be shown to represent both of these.</Paragraph>
    <Paragraph position="1"> Viewed as a method to avoid grounding an intractable number ofpredicates, this paper has similar motivations to recent work in lifted inference (Poole, 2003; de Salvo Braz et al., 2005), which performs inference directly at the first-order level to avoid instantiating all predicates. Although our model is not an instance of lifted inference, it does attempt to reduce the number of predicates by instantiating them incrementally.</Paragraph>
    <Paragraph position="2"> Identity uncertainty (also known as record linkage, deduplication, object identification, and co-reference resolution) is the problem of determining whether a set of constants (mentions) refer to the same object (entity). Successful identity resolution enables vision systems to track objects, database systems to deduplicate redundant records, and text processing systems to resolve disparate mentions of people, organizations, and locations.</Paragraph>
    <Paragraph position="3"> Many probabilistic models of object identification have been proposed in the past 40 years in databases (Fellegi and Sunter, 1969; Winkler, 1993) and natural language processing (McCarthy and Lehnert, 1995; Soon et al., 2001). With the introduction of statistical relational learning, more sophisticated models of identity uncertainty have been developed that consider the dependencies between related consolidation decisions.</Paragraph>
    <Paragraph position="4"> Most relevant to this work are the recent relational models of identity uncertainty (Milch et al., 2005; McCallum and Wellner, 2003; Parag and Domingos, 2004). McCallum and Wellner (2003) present experiments using a conditional random field that factorizes into a product of pairwise decisions about mention pairs (Model 3). These pairwise decisions are made collectively using relational inference; however, as pointed out in Milch et al. (2004), there are shortcomings to this model that stem from the fact that it does not capture features of objects, only of mention pairs. For example, aggregate features such as &amp;quot;a researcher is unlikely to publish in more than 2 different fields&amp;quot; or &amp;quot;a person is unlikely to be referred to by three different names&amp;quot; cannot be captured by solely examining pairs of mentions. Additionally, decomposing an object into a set of mention pairs results in &amp;quot;double-counting&amp;quot; of attributes, which can skew reasoning about a single object (Milch et al., 2004).</Paragraph>
    <Paragraph position="5"> Similar problems apply to the model in Parag and Domingos (2004).</Paragraph>
    <Paragraph position="6"> Milch et al. (2005) address these issues by constructing a generative probabilistic model over possible worlds called BLOG, where realizations of objects are typically sampled from a generative process. While BLOG model provides attractive semantics for reasoning about unknown objects, the transition to generatively trained models sacrifices some of the attractive properties of the discriminative model in Mc-Callum and Wellner (2003) and Parag and Domingos (2004), such as the ability to easily incorporate many overlapping features of the observed mentions.</Paragraph>
    <Paragraph position="7"> In contrast, generative models are constrained either to assume the independence of these features or to explicitly model their interactions.</Paragraph>
    <Paragraph position="8"> Object identification can also be seen as an instance of supervised clustering. Daum'e III and Marcu (2004) and Carbonetto et al. (2005) present similar Bayesian supervised clustering algorithms that use a Dirichlet process to model the number of clusters. As a generative model, it has similar advantages and disadvantages as Milch et al. (2005), with the added capability of integrating out the uncertainty in the true number of objects.</Paragraph>
    <Paragraph position="9"> In this paper, we present of identity uncertainty that incorporates the attractive properties of Mc-Callum and Wellner (2003) and Milch et al. (2005), resulting in a discriminative model to reason about objects.</Paragraph>
  </Section>
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