案例学习：预测房价

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來自 University of Washington 的課程

机器学习：回归

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案例学习：预测房价

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Multiple Regression

The next step in moving beyond simple linear regression is to consider "multiple regression" where multiple features of the data are used to form predictions. <p> More specifically, in this module, you will learn how to build models of more complex relationship between a single variable (e.g., 'square feet') and the observed response (like 'house sales price'). This includes things like fitting a polynomial to your data, or capturing seasonal changes in the response value. You will also learn how to incorporate multiple input variables (e.g., 'square feet', '# bedrooms', '# bathrooms'). You will then be able to describe how all of these models can still be cast within the linear regression framework, but now using multiple "features". Within this multiple regression framework, you will fit models to data, interpret estimated coefficients, and form predictions. <p>Here, you will also implement a gradient descent algorithm for fitting a multiple regression model.

- Emily FoxAmazon Professor of Machine Learning

Statistics - Carlos GuestrinAmazon Professor of Machine Learning

Computer Science and Engineering

[MUSIC]

Okay, well, I wanna take some time to do something that's rather boring but

it's actually very important and that's to talk about notation.

The reason it's important is because unfortunately,

there's no standard convention in the machine learning community for

how to denote the things that we're gonna be going through in this module.

And so we have chosen our notation and we really, really like it, but

it might be different than notation you've seen before.

So I want to go very slowly through this notation and what it means so

that it's very clear in the following slides when I'm using this notation,

what I mean by it.

Okay, so in this case when we're talking about multiple regression, our inputs

are a whole collection of different inputs like number of square feet,

bedrooms, bathrooms, and so on.

And we're gonna put these all together into a vector x.

And I'm gonna use this bold-faced notation to represent the fact that this is

a vector.

In some communities they might put a bar under,

a little arrow over, or there are lots of other options.

But we're gonna use bold x to denote some little d dimensional vector,

meaning there are little d different inputs in our model.

Okay, then we're going to assume that our output is just some scalar, so

that's just gonna be a normal y, no boldness to it.

Might be very bold, but it's not bold faced.

Okay, so our notational conventions are gonna be, bold x,

square brackets of j is gonna take this vector x.

And just like you would in Python, it's gonna grab out that jth element.

Okay, so the result of that is gonna be the jth input to our model, and

that's just a scalar, like number of square feet for the house.

For our features, we're gonna use these functions h that we talked about before,

so hj is our jth feature.

And in the case of multiple inputs, it might be, and we'll go through this

a little bit more in a couple slides, It might be a function of multiple inputs.

So in general, our features are a function of this bold x,

this entire d-dimensional vector.

Then, when we use bold x sub i, what we're saying is that's our ith

input, so the input associated with our ith observation,

the ith house in our data set for our housing application.

And then just to be very, very clear.

Bold x, sub i, square brackets j, means we're gonna

look at this d dimensional input vector for this ith house.

So, the number of square feet, bedrooms, bathrooms, etc., for this ith house.

And we're gonna grab out the jth input, which might be number of bathrooms.

Okay, so that's, again, just a scalar.

Okay, I said I was gonna go through that slowly.

I think I went though that slowly, but again, it's very important so

take a little snapshot of this slide.

This notation's gonna be used throughout the rest of the course.

[MUSIC]