This is due to the enormity of factors g θ (y t ; y −t ) over a large number of translation variables y t 's (i.e., the number of sentences in the document) as well as their unbounded domain (i.e., all sentences in the target language).
we resort to maximising the pseudo-likelihood (Besag, 1975) for training the parameters: where D is the set of bilingual training documents, and |d| denotes the number of (bilingual) sentences in the document .