Phrase-based MT

1. Download Koehn, PHARAOH: A Beam Search Decoder for Phrase-Based Statistical Machine Translation, and read pages 21-23 (i.e. from the start of Section 2 to the end of Section 2.2).
2. As an exercise in phrase extraction, consider the intersection alignment from Figure 3 (page 23). To keep this problem small, we will use only the part of the alignment that covers the strings "slap the green witch" and "bofetada a la bruja verde" -- that is, just the 4x5 grid in the lower right hand corner. (Don't do this exercise on the entire intersection alignment!) Apply the phrase extraction heuristic we discussed in class, i.e. extracting all phrase pairs consistent with the alignment, in order to give a table of e/f pairs.
3. Compare your table of e/f pairs with the set of phrase pairs in Figure 5 on page 25, considering only pairs from the same 4x5 sub-grid. What are the differences? Give at least one example of a phrase pair that you get from one alignment and not the other, and explain why.
4. Extra credit (20%). Consider Figure 2 on page 22. Expand the expression for p(fbar_{1..I}|ebar_{1..I}) -- i.e. the last equation just before Section 2.2 begins -- for this particular instance. This is a translation model score that includes both phrase-to-phrase translation probability and phrase distortion. You'll need to just write out phi expressions without converting them to numbers, since you don't have a phrase table with probabilities. But you can replace each instance of d(a_i - b_{i-1}) with an actual number. So the expansion will have the form: (phi(...)*d * phi(...)*d * ... * phi(...)*d) where each d is a number. (Note: for any given phrase, "start position" and "end position" refer to the positions of the first word and the last word in the phrase, respectively. E.g. "nach Kanada" has start position 4 and end position 5, assuming words are numbered from 1.)