Statistical Phrase-Based Translation

4.4 Lexical Weighting

1. What is lexical weighting of a phrase pair?
   A check of how well a pair’s words translate each other: \(p_w(\bar f \mid \bar e, a) = \prod_{i=1}^{n} \frac{1}{|\{j \mid (i,j) \in a\}|} \sum_{(i,j) \in a} w(f_i \mid e_j)\), with word probabilities \(w(f \mid e)\) by relative frequency from the same alignments. Unaligned foreign words align to NULL; with several alignments, take the highest weight.
   • Koehn et al., 2003, Statistical Phrase-Based Translation (Proceedings of the 2003 Human Language Technology Conference of the North American Chapter of ACL (HLT-NAACL 2003)), §4.4, p. 52
2. Compute the lexical weight for \(\bar f = f_1 f_2 f_3\), \(\bar e = e_1 e_2 e_3\) with alignment \(f_1\)–\(e_1\), \(f_2\)–\(e_2\), \(f_2\)–\(e_3\), \(f_3\) unaligned.
   \(p_w = w(f_1 \mid e_1) \cdot \tfrac{1}{2}\big(w(f_2 \mid e_2) + w(f_2 \mid e_3)\big) \cdot w(f_3 \mid \text{NULL})\): average over a word’s alignment points, multiply over foreign words.
   • Koehn et al., 2003, Statistical Phrase-Based Translation (Proceedings of the 2003 Human Language Technology Conference of the North American Chapter of ACL (HLT-NAACL 2003)), §4.4, p. 52
3. How is the lexical weight used in translation, and how much did it help?
   As an extra factor: \(\phi(\bar f_i \mid \bar e_i)\, p_w(\bar f_i \mid \bar e_i, a)^{\lambda}\), with \(\lambda\) around 0.25. It improved BLEU by up to 0.01, and can be precomputed into the phrase table.
   • Koehn et al., 2003, Statistical Phrase-Based Translation (Proceedings of the 2003 Human Language Technology Conference of the North American Chapter of ACL (HLT-NAACL 2003)), §4.4, p. 52