All language subtitles for 02_linear-regression-model-part-2.en

Let's look in this video at

the process of how
supervised learning works.

Supervised learning algorithm
will input a dataset and

then what exactly does it
do and what does it output?

Let's find out in this video.

Recall that a training set in

supervised learning includes
both the input features,

such as the size
of the house and

also the output targets,

such as the price of the house.

The output targets are

the right answers to the
model we'll learn from.

To train the model,

you feed the training set,

both the input features and

the output targets to
your learning algorithm.

Then your supervised
learning algorithm

will produce some function.

We'll write this
function as lowercase f,

where f stands for function.

Historically, this
function used to

be called a hypothesis,

but I'm just going to call it
a function f in this class.

The job with f is
to take a new input

x and output and estimate
or a prediction,

which I'm going to call y-hat,

and it's written like

the variable y with this
little hat symbol on top.

In machine learning,
the convention is that

y-hat is the estimate or
the prediction for y.

The function f is
called the model.

X is called the input
or the input feature,

and the output of the model
is the prediction, y-hat.

The model's prediction is
the estimated value of y.

When the symbol is
just the letter y,

then that refers to the target,

which is the actual true
value in the training set.

In contrast, y-hat
is an estimate.

It may or may not be
the actual true value.

Well, if you're
helping your client

to sell the house, well,

the true price of the house

is unknown until they sell it.

Your model f, given the size,

outputs the price which
is the estimator,

that is the prediction of
what the true price will be.

Now, when we design a
learning algorithm,

a key question is,

how are we going to
represent the function f?

Or in other words,

what is the math formula we're
going to use to compute f?

For now, let's stick with
f being a straight line.

You're function can
be written as f_w,

b of x equals,

I'm going to use w times x plus

b. I'll define w and b soon.

But for now, just know
that w and b are numbers,

and the values chosen for
w and b will determine

the prediction y-hat based
on the input feature x.

This f_w b of x

means f is a function
that takes x as input,

and depending on the
values of w and b,

f will output some value
of a prediction y-hat.

As an alternative
to writing this,

f_w, b of x,

I'll sometimes just
write f of x without

explicitly including w
and b into subscript.

Is just a simpler
notation that means

exactly the same
thing as f_w b of x.

Let's plot the training set on

the graph where the
input feature x is on

the horizontal axis and

the output target y is
on the vertical axis.

Remember, the algorithm
learns from this data and

generates the best-fit line
like maybe this one here.

This straight line is
the linear function

f_w b of x equals
w times x plus b.

Or more simply, we can
drop w and b and just

write f of x equals wx plus b.

Here's what this
function is doing,

it's making predictions
for the value of

y using a streamline
function of x.

You may ask, why are we
choosing a linear function,

where linear function is
just a fancy term for

a straight line instead of

some non-linear function
like a curve or a parabola?

Well, sometimes you want to fit

more complex non-linear
functions as well,

like a curve like this.

But since this
linear function is

relatively simple and
easy to work with,

let's use a line as

a foundation that
will eventually help

you to get to more complex
models that are non-linear.

This particular
model has a name,

it's called linear regression.

More specifically, this is

linear regression
with one variable,

where the phrase one
variable means that there's

a single input
variable or feature x,

namely the size of the house.

Another name for a
linear model with

one input variable is
univariate linear regression,

where uni means one in Latin,

and where variate
means variable.

Univariate is just a fancy
way of saying one variable.

In a later video,

you'll also see a variation
of regression where you'll

want to make a
prediction based not

just on the size of a house,

but on a bunch of other
things that you may know

about the house
such as number of

bedrooms and other features.

By the way, when you're
done with this video,

there is another optional lab.

You don't need to
write any code.

Just review it, run the
code and see what it does.

That will show you
how to define in

Python a straight line function.

The lab will let you
choose the values of

w and b to try to fit
the training data.

You don't have to do the
lab if you don't want to,

but I hope you play
with it when you're

done watching this video.

That's linear regression.

In order for you
to make this work,

one of the most important
things you have to do

is construct a cost function.

The idea of a cost
function is one of

the most universal
and important ideas

in machine learning,

and is used in both
linear regression and in

training many of the most

advanced AI models in the world.

Let's go on to the next
video and take a look

at how you can construct
a cost function.