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