Okay, so in this next segment of the class we're going to talk about the IBM translation models. The IBM models go back to the late 19, 1980s, early 1990s. They were seminal in really starting the whole statistical approach to the translation problem. They form a central part of modern statistical translation systems, and so we'll cover these models in some detail in the segment of the class. So just to recap, this is a slide from the last segment of this class. This is a recap of a noisy channel model. Which was introduced by the IBM researches to translation. So a noisy channel model, as we said, has two components. Firstly, p of e, this is a language model, this is a model that assigns a probability to any sentence in English. And secondly, p of f given e. So this is what's called the translation model. This assigns the model for a French sentence given an English sentence. One note. Throughout this lecture, I'll follow convention which is, I'll always assume that we're translating from a French sentence to an English sentence. So that is our goal. Okay. Of course, we might have other languages for translating between. But for the purposes of this lecture, we'll always assume we're translating from French to English. Okay, so we have a language model for strings in English. We have a translation model which, as I said, is in a sense backwards. It says what's the conditional probability of any French sentence, given an English sentence. When we translate on to this model we search for the English sentence that maximizes the product of p of e and p of f given e. And so when we evaluate for particular sentence f. Different English translations, we take both of these terms into account. So, the roadmap for the next few lectures in this course on translation is as follows. I'm first going to describe IBM Models 1 and 2. So IBM went through a series of models, I think 1 through 5, and we're just going to do the first two because they will essentially introduce many of the important ideas. And actually model 2 is a pretty decent model for the problem we're going to be looking at. We'll then go on to describe phrase-based models. So phrased-based models were invented around the late 1990s, and they're in some sense a second generation of s-, school translation systems. This is the first generation. They make direct use of ideas from these IBM models, and so these IBM models will, in some sense, form a basis of phrase-based models, but phrase-based models work much, much better than IBM models. They do, in fact form the basis of many modern statistical translation systems, so for example, Google translate is heavily built on this technology. So, we'll first talk about IBM Model 1 and then we'll talk about IBM Model 2 and then finally we'll talk about parameter estimation in models 1 and 2. How do we actually learn the parameters of these models? From data consisting of example translations.