The Mathematics of Statistical Machine Translation: Parameter Estimation

4.6 Model 4

1. What problem with Model 3’s distortion does Model 4 fix?
   Phrases tend to move as units, but Model 3 moves each word independently, so moving a long phrase is much less likely than a short one. Model 4 makes placement relative: the head (leftmost word) of a cept is placed relative to the center of the previous cept, and other words relative to the previous word of the same cept.
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §4.6
2. How does Model 4 capture French adjective–noun order?
   Head displacement probabilities depend on word classes of the previous English cept and the French word (50 classes each, from a mutual-information clustering). Trained values: \(d_1(-1 \mid A(\text{government’s}), B(\text{développement})) = 0.80\) vs 0.02 for \(+1\).
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §4.6
3. How does Model 4 treat words of the same cept that belong together vs apart?
   Non-head words are placed relative to the previous word of the cept, in order. Implemented → mis en application stays contiguous, while not → ne … pas usually has a verb in between, so \(d_{>1}(2 \mid B(pas))\) is large (0.68).
   • Brown et al., 1993, The Mathematics of Statistical Machine Translation (Computational Linguistics), §4.6