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We will be discussing the classic paper which kickstarted the area of Statistical Machine Translation.

http://www.ling.upenn.edu/courses/Spring_2011/cogs502/Brown1990.pdf

The following is a explanatory document discussing the translation models, EM algorithm and provides mathematical proofs: http://www.cs.columbia.edu/~mcollins/courses/nlp2011/notes/ibm12.pdf

And finally, these are slides discussing the same material but with more examples and easier to understand: http://www.statmt.org/book/slides/04-word-based-models.pdf

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