All language subtitles for 01_feature-scaling-part-1.en

So welcome back.

Let's take a look at some techniques that
make great inter sense work much better.

In this video you see a technique
called feature scaling that will enable

gradient descent to run much faster.

Let's start by taking a look at
the relationship between the size of

a feature that is how big
are the numbers for that feature and

the size of its associated parameter.

As a concrete example, let's predict
the price of a house using two

features x1 the size of the house and
x2 the number of bedrooms.

Let's say that x1 typically ranges
from 300 to 2000 square feet.

And x2 in the data set
ranges from 0 to 5 bedrooms.

So for this example, x1 takes on
a relatively large range of values and

x2 takes on a relatively
small range of values.

Now let's take an example of a house
that has a size of 2000 square

feet has five bedrooms and
a price of 500k or $500,000.

For this one training example,
what do you think

are reasonable values for
the size of parameters w1 and w2?

Well, let's look at one
possible set of parameters.

Say w1 is 50 and w2 is 0.1 and

b is 50 for the purposes of discussion.

So in this case the estimated
price in thousands

of dollars is 100,000k
here plus 0.5 k plus 50 k.

Which is slightly over
100 million dollars.

So that's clearly very far from
the actual price of $500,000.

And so this is not a very good set
of parameter choices for w1 and w2.

Now let's take a look
at another possibility.

Say w1 and w2 were the other way around.

W1 is 0.1 and w2 is 50 and
b is still also 50.

In this choice of w1 and w2,
w1 is relatively small and

w2 is relatively large,
50 is much bigger than 0.1.

So here the predicted price is 0.1 times

2000 plus 50 times five plus 50.

The first term becomes 200k, the second
term becomes 250k, and the plus 50.

So this version of the model predicts
a price of $500,000 which is a much more

reasonable estimate and happens to be the
same price as the true price of the house.

So hopefully you might notice that when
a possible range of values of a feature

is large, like the size and square feet
which goes all the way up to 2000.

It's more likely that a good model will
learn to choose a relatively small

parameter value, like 0.1.

Likewise, when the possible
values of the feature are small,

like the number of bedrooms,
then a reasonable value for

its parameters will be
relatively large like 50.

So how does this relate
to grading descent?

Well, let's take a look at
the scatter plot of the features

where the size square feet is
the horizontal axis x1 and

the number of bedrooms exudes
is on the vertical axis.

If you plot the training data, you notice
that the horizontal axis is on a much

larger scale or much larger range of
values compared to the vertical axis.

Next let's look at how the cost
function might look in a contour plot.

You might see a contour plot where the
horizontal axis has a much narrower range,

say between zero and one,
whereas the vertical axis takes on much

larger values, say between 10 and 100.

So the contours form ovals or ellipses and

they're short on one side and
longer on the other.

And this is because a very small change
to w1 can have a very large impact

on the estimated price and
that's a very large impact on the cost J.

Because w1 tends to be multiplied
by a very large number,

the size and square feet.

In contrast,

it takes a much larger change in w2 in
order to change the predictions much.

And thus small changes to w2, don't
change the cost function nearly as much.

So where does this leave us?

This is what might end up happening
if you were to run great in dissent,

if you were to use your
training data as is.

Because the contours are so tall and

skinny gradient descent may end
up bouncing back and forth for

a long time before it can finally
find its way to the global minimum.

In situations like this, a useful
thing to do is to scale the features.

This means performing some
transformation of your training data so

that x1 say might now range from 0 to
1 and x2 might also range from 0 to 1.

So the data points now look more like this
and you might notice that the scale of

the plot on the bottom is now quite
different than the one on top.

The key point is that the re scale x1 and

x2 are both now taking comparable
ranges of values to each other.

And if you run gradient descent on
a cost function to find on this,

re scaled x1 and x2 using this
transformed data, then the contours

will look more like this more like
circles and less tall and skinny.

And gradient descent can find a much
more direct path to the global minimum.

So to recap, when you have different
features that take on very different

ranges of values, it can cause
gradient descent to run slowly but

re scaling the different features so they
all take on comparable range of values.

because speed, upgrade and
dissent significantly.

How do you actually do this?

Let's take a look at
that in the next video.