1.1 Machine learning lecture 2  (Page 3/15)

Instructor (Andrew Ng) :All right, so who thought driving could be that dramatic, right? Switch back to the chalkboard, please. I should say, this work was done about 15 years ago and autonomous driving has come a long way. So many of you will have heard of the DARPA Grand Challenge, where one of my colleagues, Sebastian Thrun, the winning team's drive a car across a desert by itself.

So Alvin was, I think, absolutely amazing work for its time, but autonomous driving has obviously come a long way since then. So what you just saw was an example, again, of supervised learning, and in particular it was an example of what they call the regression problem, because the vehicle is trying to predict a continuous value variables of a continuous value steering directions, we call the regression problem.

And what I want to do today is talk about our first supervised learning algorithm, and it will also be to a regression task. So for the running example that I'm going to use throughout today's lecture, you're going to return to the example of trying to predict housing prices. So here's actually a dataset collected by TA, Dan Ramage, on housing prices in Portland, Oregon.

So here's a dataset of a number of houses of different sizes, and here are their asking prices in thousands of dollars, $200,000. And so we can take this data and plot it, square feet, best price, and so you make your other dataset like that. And the question is, given a dataset like this, or given what we call a training set like this, how do you learn to predict the relationship between the size of the house and the price of the house?

So I'm actually going to come back and modify this task a little bit more later, but let me go ahead and introduce some notation, which I'll be using, actually, throughout the rest of this course. The first piece of notation is I'm going to let the lower case alphabet M denote the number of training examples, and that just means the number of rows, or the number of examples, houses, and prices we have.

And in this particular dataset, we have, what actually happens, we have 47 training examples, although I wrote down only five. Okay, so throughout this quarter, I'm going to use the alphabet M to denote the number of training examples. I'm going to use the lower case alphabet X to denote the input variables, which I'll often also call the features. And so in this case, X would denote the size of the house they were looking at.

I'm going to use Y to denote the "output" variable, which is sometimes also called a target variable, and so one pair, x, y, is what comprises one training example. In other words, one row on the table I drew just now what would be what I call one training example, and the Ith training example, in other words the Ith row in that table, I'm going to write as XI, Y, I.

Okay, and so in this notation they're going to use this superscript I is not exponentiation. So this is not X to the power of IY to the power of I. In this notation, the superscript I in parentheses is just sort of an index into the Ith row of my list of training examples.