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Large-Scale Semi-Supervised Learning for Natural Language ...

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sets of cognates across groups of languages. We showed improvements over simple clusteringtechniques that do not inherently consider the transitivity of cognate relations. Wedeveloped our multi-lingual approach via the global inference framework of integer linearprogramming. We followed Roth and Yih [2004] in using binary-{0,1} ILP variables torepresent the decisions made by our system (cognate or not a cognate), and we optimized asour objective function the sum of the costs/scores of the decisions, with constraints <strong>for</strong> transitivityand one-to-one mappings across languages. Our <strong>for</strong>mulation was partly based onsimilar solutions <strong>for</strong> other tasks by [Barzilay and Lapata, 2006; Denis and Baldridge, 2007].Application of these techniques should improve the detection of translated sentences as well[Munteanu and Marcu, 2005], since transitivity across languages also applies, of course, atthe sentence level.107

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