All language subtitles for 06_polynomial-regression.en

So far we've just been

fitting straight
lines to our data.

Let's take the ideas of
multiple linear regression and

feature engineering
to come up with

a new algorithm called
polynomial regression,

which will let you fit curves,

non-linear functions,
to your data.

Let's say you have a housing

data-set that looks like this,

where feature x is the
size in square feet.

It doesn't look like
a straight line

fits this data-set very well.

Maybe you want to fit a curve,

maybe a quadratic
function to the data like

this which includes a size
x and also x squared,

which is the size raised
to the power of two.

Maybe that will give you
a better fit to the data.

But then you may decide that

your quadratic model
doesn't really make sense

because a quadratic function
eventually comes back down.

Well, we wouldn't really expect

housing prices to go down
when the size increases.

Big houses seem like they
should usually cost more.

Then you may choose a
cubic function where we

now have not only x
squared, but x cubed.

Maybe this model produces
this curve here,

which is a somewhat
better fit to

the data because the size

does eventually come back
up as the size increases.

These are both examples
of polynomial regression,

because you took your
optional feature x,

and raised it to the power of

two or three or any other power.

In the case of the
cubic function,

the first feature is the size,

the second feature
is the size squared,

and the third feature
is the size cubed.

I just want to point
out one more thing,

which is that if you
create features that are

these powers like the square

of the original
features like this,

then feature scaling becomes
increasingly important.

If the size of the
house ranges from say,

1-1,000 square feet,

then the second feature,

which is a size squared,

will range from
one to a million,

and the third feature,

which is size cubed,

ranges from one to a billion.

These two features, x
squared and x cubed,

take on very different ranges of

values compared to the
original feature x.

If you're using
gradient descent,

it's important to apply
feature scaling to get

your features into
comparable ranges of values.

Finally, just one last
example of how you

really have a wide range of
choices of features to use.

Another reasonable
alternative to

taking the size squared and

size cubed is to say use
the square root of x.

Your model may look
like w_1 times

x plus w_2 times the
square root of x plus b.

The square root function
looks like this,

and it becomes a bit less
steep as x increases,

but it doesn't ever
completely flatten out,

and it certainly never
ever comes back down.

This would be another
choice of features that

might work well for
this data-set as well.

You may ask yourself,

how do I decide what
features to use?

Later in the second course
in this specialization,

you see how you can choose
different features and

different models that include

or don't include these features,

and you have a process
for measuring how well

these different models
perform to help you

decide which features to
include or not include.

For now, I just want
you to be aware

that you have a choice in
what features you use.

By using feature engineering
and polynomial functions,

you can potentially get

a much better model
for your data.

In the optional lab that
follows this video,

you will see some
code that implements

polynomial regression
using features like x,

x squared, and x cubed.

Please take a look and run the
code and see how it works.

There's also another
optional lab

after that one that shows how to

use a popular open
source toolkit

that implements
linear regression.

Scikit-learn is

a very widely used open source
machine learning library

that is used by
many practitioners

in many of the top AI,

internet, machine learning
companies in the world.

If either now or in the future

you're using machine
learning in your job,

there's a very good
chance you'll be using

tools like Scikit-learn
to train your models.

Working through that
optional lab will give you

a chance to not only better
understand linear regression,

but also see how
this can be done in

just a few lines of code using

a library like Scikit-learn.

For you to have a
solid understanding

of these algorithms,

and be able to apply them,

I do think is important that you

know how to implement
linear regression

yourself and not just call

some scikit-learn function
that is a black-box.

But scikit-learn also has

an important role in a way

machine learning is
done in practice today.

We're just about at
the end of this week.

Congratulations on finishing
all of this week's videos.

Please do take a
look at the practice

quizzes and also
the practice lab,

which I hope will
let you try out and

practice ideas that
we've discussed.

In this week's practice lab,

you implement linear regression.

I hope you have a
lot of fun getting

this learning algorithm
to work for yourself.

Best of luck with that.

I also look forward to seeing
you in next week's videos,

where we'll go
beyond regression,

that is predicting numbers,

to talk about our first
classification algorithm,

which can predict categories.

I'll see you next week.