Translation model that considers how a word can be aligned to multiple words in another language.
IBM Model 3 improves on Model 2 by directly modeling the phenomenon where a word in one language may be translated into zero or more words in another. This is expressed by the fertility probability, n(phi | source word).
If a source word translates into more than one word, it is possible to generate sentences that have the same alignment in multiple ways. This is modeled by a distortion step. The distortion probability, d(j|i,l,m), predicts a target word position, given its aligned source word's position. The distortion probability replaces the alignment probability of Model 2.
The fertility probability is not applicable for NULL. Target words that align to NULL are assumed to be distributed uniformly in the target sentence. The existence of these words is modeled by p1, the probability that a target word produced by a real source word requires another target word that is produced by NULL.
The EM algorithm used in Model 3 is: E step - In the training data, collect counts, weighted by prior
probabilities. (a) count how many times a source language word is translated
into a target language word
- count how many times a particular position in the target sentence is aligned to a particular position in the source sentence
- count how many times a source word is aligned to phi number of target words
- count how many times NULL is aligned to a target word
M step - Estimate new probabilities based on the counts from the E step
Because there are too many possible alignments, only the most probable ones are considered. First, the best alignment is determined using prior probabilities. Then, a hill climbing approach is used to find other good candidates.
Notations: i: Position in the source sentence
Valid values are 0 (for NULL), 1, 2, ..., length of source sentence
- j: Position in the target sentence
- Valid values are 1, 2, ..., length of target sentence
l: Number of words in the source sentence, excluding NULL m: Number of words in the target sentence s: A word in the source language t: A word in the target language phi: Fertility, the number of target words produced by a source word p1: Probability that a target word produced by a source word is
accompanied by another target word that is aligned to NULL
p0: 1 - p1
References: Philipp Koehn. 2010. Statistical Machine Translation. Cambridge University Press, New York.
Peter E Brown, Stephen A. Della Pietra, Vincent J. Della Pietra, and Robert L. Mercer. 1993. The Mathematics of Statistical Machine Translation: Parameter Estimation. Computational Linguistics, 19 (2), 263-311.
| Class | |
Translation model that considers how a word can be aligned to multiple words in another language |
| Class | |
Data object to store counts of various parameters during training. Includes counts for distortion. |