Machine learning lecture 1  (Page 12/17)

So, for example, what a learning algorithm may do is maybe come in and decide that a straight line like that separates the two classes of tumors really well, and so if you have a new patient who's age and tumor size fall over there, then the algorithm may predict that the tumor is benign rather than malignant, okay? So this is just another example of another supervised learning problem and another classification problem.

And so it turns out that one of the issues we'll talk about later in this class is in this specific example, we're going to try to predict whether a tumor is malignant or benign based on two features or based on two inputs, namely the age of the patient and the tumor size. It turns out that when you look at a real data set, you find that learning algorithms often use other sets of features. In the breast cancer data example, you also use properties of the tumors, like clump thickness, uniformity of cell size, uniformity of cell shape, [inaudible] adhesion and so on, so various other medical properties.

And one of the most interesting things we'll talk about later this quarter is what if your data doesn't lie in a two-dimensional or three-dimensional or sort of even a finite dimensional space, but is it possible — what if your data actually lies in an infinite dimensional space? Our plots here are two-dimensional space. I can't plot you an infinite dimensional space, right? And so it turns out that one of the most successful classes of machine learning algorithms — some may call support vector machines — actually takes data and maps data to an infinite dimensional space and then does classification using not two features like I've done here, but an infinite number of features.

And that will actually be one of the most fascinating things we talk about when we go deeply into classification algorithms. And it's actually an interesting question, right, so think about how do you even represent an infinite dimensional vector in computer memory? You don't have an infinite amount of computers. How do you even represent a point that lies in an infinite dimensional space? We'll talk about that when we get to support vector machines, okay?

So let's see. So that was supervised learning. The second of the four major topics of this class will be learning theory. So I have a friend who teaches math at a different university, not at Stanford, and when you talk to him about his work and what he's really out to do, this friend of mine will — he's a math professor, right? — this friend of mine will sort of get the look of wonder in his eyes, and he'll tell you about how in his mathematical work, he feels like he's discovering truth and beauty in the universe. And he says it in sort of a really touching, sincere way, and then he has this — you can see it in his eyes — he has this deep appreciation of the truth and beauty in the universe as revealed to him by the math he does.

In this class, I'm not gonna do any truth and beauty. In this class, I'm gonna talk about learning theory to try to convey to you an understanding of how and why learning algorithms work so that we can apply these learning algorithms as effectively as possible.