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\sum_x t'(e_x | f_y) = 1 \quad \forall y
\end{cases}
</math>This can be solved by [[Lagrange multiplier|Lagrangian multipliers]], then simplified. For a detailed derivation of the algorithm, see <ref name=":0">{{Cite book |last=Koehn |first=Philipp |url=https://books.google.com/books?id=4v_Cx1wIMLkC&newbks=0&hl=en |title=Statistical Machine Translation |date=2010 |publisher=Cambridge University Press |isbn=978-0-521-87415-1 |language=en |chapter=4. Word-Based Models}}</ref> chapter 4 and
In short, the EM algorithm goes as follows:<blockquote>INPUT. a corpus of English-foreign sentence pairs <math>\{(e^{(k)}, f^{(k)})\}_k</math>
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