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So finally to summarize some key ideas we
saw in the IBM translation models.

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Really the single key idea was to
introduce these alignment variables,

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specifying how words in one language are
aligned with words in another language.

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And second to make use of translation
parameters.

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For example the probability that dog is
translated to the word chien.

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And also distortion parameters.
For example the probability of the

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position one in French is aligned to
position two in English.

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We saw this parameter estimation
algorithm, the EM algorithm.

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So this is an iterative algorithm for
training the Q and T parameters.

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It starts off with some initial values for
q and t, and then recalculates them using

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the method I described.
And we typically run this for several

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iterations, or until convergence.
And critically, once I have recovered

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these q and t parameters using the EM
algorithm.

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I can go back to my training examples and
fill in alignments.

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So earlier I showed you how we can recover
the most likely alignment for a sentence.

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Once we have the Q and T parameters.
And this is actually how the idea models

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currently use the machine translations
systems.

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They are a critical component in that they
allow us to recover these alignments in

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our training examples.
And in the next lecture of this course,

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we'll talk about phrase-based systems.
And phrase-based systems are going to make

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very direct use of the alignments which
are recovered using the IBM models.