More precisely, we use pivoting to estimate the probability Pr(w ′ |w) as follows: Then, following (Callison-Burch et al., 2006;Wu and Wang, 2007), we make the simplifying assumption that w ′ is conditionally independent of w given e i , thus obtaining the following expression: We estimate the probability Pr(e i |w) directly from the word-aligned training bi-text as follows: where #(x, e) is the number of times the Malay word x is aligned to the English word e. Estimating Pr(w ′ |e i ) cannot be done directly since w ′ might not be present on the Malay side of the training bi-text, e.g., because it is a multi-token sequence generated by clitic segmentation.
we think of w ′ as a pseudoword that stands for the union of all Malay words in the training bi-text that are reducible to w ′ by our morphological analysis procedure.