So finally to summarize some key ideas we saw in the IBM translation models. Really the single key idea was to introduce these alignment variables, specifying how words in one language are aligned with words in another language. And second to make use of translation parameters. For example the probability that dog is translated to the word chien. And also distortion parameters. For example the probability of the position one in French is aligned to position two in English. We saw this parameter estimation algorithm, the EM algorithm. So this is an iterative algorithm for training the Q and T parameters. It starts off with some initial values for q and t, and then recalculates them using the method I described. And we typically run this for several iterations, or until convergence. And critically, once I have recovered these q and t parameters using the EM algorithm. I can go back to my training examples and fill in alignments. So earlier I showed you how we can recover the most likely alignment for a sentence. Once we have the Q and T parameters. And this is actually how the idea models currently use the machine translations systems. They are a critical component in that they allow us to recover these alignments in our training examples. And in the next lecture of this course, we'll talk about phrase-based systems. And phrase-based systems are going to make very direct use of the alignments which are recovered using the IBM models.