案例学习：预测房价

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From the course by University of Washington

机器学习：回归

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案例学习：预测房价

From the lesson

Simple Linear Regression

Our course starts from the most basic regression model: Just fitting a line to data. This simple model for forming predictions from a single, univariate feature of the data is appropriately called "simple linear regression".<p> In this module, we describe the high-level regression task and then specialize these concepts to the simple linear regression case. You will learn how to formulate a simple regression model and fit the model to data using both a closed-form solution as well as an iterative optimization algorithm called gradient descent. Based on this fitted function, you will interpret the estimated model parameters and form predictions. You will also analyze the sensitivity of your fit to outlying observations.<p> You will examine all of these concepts in the context of a case study of predicting house prices from the square feet of the house.

- Emily FoxAmazon Professor of Machine Learning

Statistics - Carlos GuestrinAmazon Professor of Machine Learning

Computer Science and Engineering

Now that we have an understanding of what the fitted line is, and how we can use it,

let's talk about an algorithm, or really algorithms for searching out the space of

all possible lines that we might use, and finding the one that best fits the data.

So in particular what we're going to be doing is focusing in on this machine

learning algorithm, which is this dark gray square shown in this flow chart.

Okay, so recall that our cost was to find us this residual sum of squares,

and for any given line, we can compute the cost of that line.

So, for example, we showed three different lines and

three different residual sum of squares here, but

our goal was to minimize over all possible W0 and W1 slopes and

intercepts, but a question is, how are we going to do this?

So that's the key question that we're looking to address in this

part of the module.

Let's formalize this idea a little bit more.

So here, what we're showing is our residual sum of squares and

what we see is it's a function of two variables, w0 and w1.

So we can write it generically,

let's just write it as some function g of a variable w0 and a variable w1.

And what I've done is I've gone ahead and

plotted the residual sum of squares versus w zero and w one for

the data set you guys played within the first course of this specialization.

So here along this axis is w zero and along this axis is w one.

And then we are plotting here our residual sum of squares.

And that is this blue mesh surface here, that's

our residual sum of squares for any given w zero, w one pair.

And our objective here is to minimize over all possible combinations of w zero,

and w one, so mathematically we write that, great, I wrote right over what I

wanted to show you guys, so let me erase what I wrote before, and

rewrite it so that it's a little bit more intelligible.

But, as I was saying, our mathematical notation for this minimization over

all possible W0, W1 is this notation right here.

Okay, so in terms of the picture what we want to do is

over this entire space of w zero and w one, we want to find the place,

let me find the place so that this is a little easier to see on this slide,

so we want to find the specific value of W0.

So, we'll call that W0 hat.

And W1 hat, that minimize this residual summit squares.

So, this is our objective.

And switching back to our blue color here, this is an optimization problem,

where specifically the optimization objective is to minimize a function,

in this case, of two parameters, two different variables.

[MUSIC]

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