C is our unique pre-terminal for generating terminal multi-word pairs: We parameterize our probabilistic model in the manner of a PCFG: we associate a multinomial distribution with each nonterminal, where each outcome in this distribution corresponds to an expansion of that nonterminal.
specifically, we place one multinomial distribution θ X over the three expansions of the nonterminal X, and another multinomial distribution θ C over the expansions of C. the parameters in our model can be listed as where P is for the inverted rule, P [] for the straight rule, P C for the third rule, satisfying P +P [] +P C = 1, and where e/f P (e/f ) = 1 is a multinomial distribution over phrase pairs.