Definitions | Intuitively, propemess ensures that where a pair of nonterminals in two synchronous strings can be rewritten, there is a probability distribution over the applicable rules. |
Definitions | We say a PSCFG is consistent if pg defines a probability distribution over the translation, or formally: |
Discussion | Prefix probabilities and right prefix probabilities for PSCFGs can be exploited to compute probability distributions for the next word or part-of-speech in left-to-right incremental translation of speech, or alternatively as a predictive tool in applications of interactive machine translation, of the kind described by Foster et al. |
Effective PSCFG parsing | The translation and the associated probability distribution in the resulting grammar will be the same as those in the source grammar. |
Effective PSCFG parsing | Again, in the resulting grammar the translation and the associated probability distribution will be the same as those in the source grammar. |
Introduction | Prefix probabilities can be used to compute probability distributions for the next word or part-of-speech. |
Introduction | Prefix probabilities and right prefix probabilities for PSCFGs can be exploited to compute probability distributions for the next word or part-of-speech in left-to-right incremental translation, essentially in the same way as described by Jelinek and Lafferty (1991) for probabilistic context-free grammars, as discussed later in this paper. |
Prefix probabilities | The next step will be to transform Qprefix into a third grammar gl’mfix by eliminating epsilon rules and unit rules from the underlying SCFG, and preserving the probability distribution over pairs |
Experimental Setup | Table 2: Key to probability distributions |
Experimental Setup | Table 2 is a key to the probability distributions we use. |
Introduction | Language models, probability distributions over strings of words, are fundamental to many applications in natural language processing. |
Abstract | The log linear model is defined as a conditional probability distribution of a corrected word and a rule set for the correction conditioned on the misspelled word. |
Introduction | The log linear model is defined as a conditional probability distribution of a corrected word and a rule set for the correction given the misspelled word. |
Model for Candidate Generation | We define the conditional probability distribution of we and R(wm, we) given mm as the following log linear model: |