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机器学习吴恩达cs229原版讲义 Supervised learning Lets start by talking about a few examples of supervised learning problems. Suppose we have a dataset giving the living areas and prices of 47 houses from Portland, Oregon: Living area (feet2) Price (1000$s) 2104 400 1600 330 2400 369 1416 232 3000 540 . . . . . . We can plot this data: 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 0 100 200 300 400 500 600 700 800 900 1000 housing prices square feet price (in $1000) Given data like this, how can we learn to predict the prices of other houses in Portland, as a function of the size of their living areas? 1 CS229 Winter 2003 2 To establish notation for future use, we’ll use x(i) to denote the “input” variables (living area in this example), also called input features, and y(i) to denote the “output” or target variable that we are trying to predict (price). A pair (x(i),y(i)) is called a training example, and the dataset that we’ll be using to learn—a list of m training examples {(x(i),y(i));i = 1,...,m}—is called a training set. Note that the superscript “(i)” in the notation is simply an index into the training set, and has nothing to do with exponentiation. We will also use X denote the space of input values, and Y the space of output values. In this example, X = Y = R. To describe the supervised learning problem slightly more formally, our goal is, given a training set, to learn a function h : X 7→Y so that h(x) is a “good” predictor for the corresponding value of y. For historical reasons, this function h is called a hypothesis. Seen pictorially, the process is therefore like this