案例学习：预测房价

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来自 University of Washington 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

Welcome

Regression is one of the most important and broadly used machine learning and statistics tools out there. It allows you to make predictions from data by learning the relationship between features of your data and some observed, continuous-valued response. Regression is used in a massive number of applications ranging from predicting stock prices to understanding gene regulatory networks.<p>This introduction to the course provides you with an overview of the topics we will cover and the background knowledge and resources we assume you have.

- Emily FoxAmazon Professor of Machine Learning

Statistics - Carlos GuestrinAmazon Professor of Machine Learning

Computer Science and Engineering

[MUSIC]

This course consists of six different modules,

and let's preview what these are about.

To start with, we're gonna talk about simple regression, and

why is it called simple regression?

That's because we're gonna focus on just having a single input, for

example the size of your house and when we think about defining

the relationship between the single input and our output, the house sales price,

we're just gonna look at fitting a very simple line to this data.

And that's why it's called simple regression.

And one thing we're gonna need to do in order to discover what the best fitted

line is is we're gonna need to define something called a goodness-of-fit metric

that allows us to say that some lines fit better than other lines and

according to this metric we can then search over all possible lines to find

the one that fits the data the best.

So in this context of this goodness-of-fit metric we're then going to discuss some

important optimization techniques that are much more general than regression itself.

So this is an example of one of these general concepts that we're going to see

again, many times in the specialization.

And the method that we're going to explore here is something called gradient decent.

So in the context of our regression problem, and

we have just a simple line, a question is well what's the slope and

what's the intercept of this line that minimizes this goodness-of-fit metric.

So this blue curve I'm showing here is showing how good the fit is,

where lower means actually a better fit and we're gonna try and

minimize over all possible combinations of intercepts and slopes.

To find the once that fits best.

This gradient descent algorithm is an iterative algorithm that's gonna take

multiple steps.

And eventually go to this optimal solution that minimizes this metric.

Measuring how well this line fits.

Then once we've found this minimum, so we've found the best intercepting slope,

what we're gonna talk about is how to think about interpreting these

estimated parameters, and then how to use these parameters to form our predictions.

We're then gonna move from simple regression to multiple regression, and

multiple regression allows us to fit more complicated relationships

between our single input and an output.

So, more complicated than just a line as well as to consider

more inputs in our model.

So, for our housing application,

maybe in addition to measure up the size of the house,

we have something talking about how many bedrooms there are, how many bathrooms.

What the lot size is,

what year the house was built and we might have a whole bunch of different

attributes of the house that we wanna incorporate into forming our predictions.

And that's what multiple regression allows us to do.

Having learned how to fit these models to data, we're then gonna turn to

how to assess whether the fin is any good for example in forming predictions.

For example, this fit shown here between house size and

house price seems to be pretty good, but if we go to a much more complicated model,

we see that it's doing really crazy things, but if you look carefully this

fitted function is actually explaining our observed data these circles really well.

But what it's not doing is it's not able to generalize

to predictions of new houses that we haven't observed,

because at least I wouldn't use this to form predictions of my house value.

I wouldn't really believe that this is the relationship between house size and price.

So question is, what's going wrong here?

And this is something that we call over fitting to the data,

and we're gonna talk about this in great length in this module of the course.

In particular we're gonna define three different measures of air.

One called training air, one is called test air, and

one is called our generalization or true air, and

that's actually the air we really want to form, but we're gonna show that

that is something that we can't actually attain and we have to use proxies instead.

And we're gonna look at these measures of error

as a function of model complexity to describe this notion of over-fitting.

Then we're gonna discuss these ideas in the context of something called

the bias-variance trade-off and what this describes is the fact that

simple models tend to be really well behaved but they're

often just too simple to really describe the relationship that we're interested in.

On the other hand, really complex models are really flexible, so

they have the potential to fit really intricate relationships that might

describe pretty well what's happening with the data but unfortunately these really,

really complex models can have very strange behavior.

And so this leads to what's called this bias-variance trade-off.

And machine learning is all about exploring this trade off.

[MUSIC]