Lexical translation model that ignores word order.
In IBM Model 1, word order is ignored for simplicity. As long as the word alignments are equivalent, it doesn't matter where the word occurs in the source or target sentence. Thus, the following three alignments are equally likely.
Source: je mange du jambon Target: i eat some ham Alignment: (0,0) (1,1) (2,2) (3,3)
Source: je mange du jambon Target: some ham eat i Alignment: (0,2) (1,3) (2,1) (3,1)
Source: du jambon je mange Target: eat i some ham Alignment: (0,3) (1,2) (2,0) (3,1)
Note that an alignment is represented here as (word_index_in_target, word_index_in_source).
The EM algorithm used in Model 1 is: E step - In the training data, count how many times a source language
word is translated into a target language word, weighted by the prior probability of the translation.
- M step - Estimate the new probability of translation based on the
- counts from the Expectation step.
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
s: A word in the source language t: A word in the target language
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.
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Lexical translation model that ignores word order |