We present a probabilistic model for constraint-based grammars and a methodfor estimating the parameters of such models from incomplete, i.e., unparseddata. Whereas methods exist to estimate the parameters of probabilisticcontext-free grammars from incomplete data (Baum 1970), so far forprobabilistic grammars involving context-dependencies only parameter estimationtechniques from complete, i.e., fully parsed data have been presented (Abney1997). However, complete-data estimation requires labor-intensive, error-prone,and grammar-specific hand-annotating of large language corpora. We present alog-linear probability model for constraint logic programming, and a generalalgorithm to estimate the parameters of such models from incomplete data byextending the estimation algorithm of Della-Pietra, Della-Pietra, and Lafferty(1997) to incomplete data settings.
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