案例学习：预测房价

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来自 华盛顿大学 的课程

机器学习：回归

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案例学习：预测房价

从本节课中

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]

So we talked about polynomial regression,

where you have different powers of your input.

And we also talked about seasonality where you have these sine and cosine bases.

But we can really think about any function of our single input.

So let's write down our

model a little bit more generically in terms of some set of features.

And I'm gonna denote each one of my features with this function H.

So H0 is gonna be my first feature,

H1 my second feature, H capital D, my last feature.

So we can more compactly represent this model

using the sigma notation that we introduced previously.

Where we put an index I equals one to capital D.

Saying we're summing over each of these capital D different features.

And just to be very clear h sub j of x is our jth feature,

and wj is the regression coefficient or weight associated with that feature.

So just to give some examples that we've gone through, this first feature might

just be one, this constant feature that we've used in all of the past examples.

Or when we think about our second feature, h1, maybe that's just our linear term, x.

Our third feature might be x squared or maybe it's our sine basis.

Or we could think of lots of other feature examples and

when we get to our capital Dth feature, maybe it's just our

input raised to the pth power when we're thinking about polynomial regression.

So, going back to our regression flow chart or

block diagram here, we kinda swept something under the rug before.

We never really highlighted this blue feature extraction box,

and we just said the output of it was x.

Really, now that we've learned a little bit more about regression and this

notion of features, really the output of this feature extraction is not x but h(x).

It's our features of our input x.

So x is really the input to our feature extractor, and

the output is some set of functions of x.

So for the remainder of this course,

we're gonna assume that the output of this feature extraction box is h of x.

[MUSIC]