统计机器学习（斯坦福大学讲义）1-12(全).pdf

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CS229 Lecture notes

Andrew Ng

Supervised learni ng

Let’s 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 (feet

)

Price (1000$s)

2104 400

1600 330

2400 369

1416

232

3000 540

We can plot t his data:

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

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 ot her houses

in Portland, as a function of the size of their living areas?

CS229 Fall 2012 2

To establish notation for future use, we’ll use x

(i)

to denote the “ input”

variables (living a r ea in this example), also called input features, and y

(i)

to denote the “output” o r target variable that we are trying to predict

(price). A pair (x

(i)

, y

(i)

) is called a training example, and the data set

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 int o the training set, and has nothing to do with

exp onentiation. 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:

Training

set

house.)

(living area of

Learning

algorithm

predicted yx

(predicted price)

of house)

When the target variable t hat we’re trying to predict is continuous, such

as in our housing example, we call the learning problem a regression prob-

lem. When y can take on only a small number of discrete values (such as

if, given the living area, we wanted t o predict if a dwelling is a house or an

apartment, say), we call it a classiﬁcation problem.

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