All language subtitles for 06_visualization-examples.en

Let's look at some
more visualizations of

w and b. Here's one example.

Over here, you have a particular
point on the graph j.

For this point, w
equals about negative

0.15 and b equals about 800.

This point corresponds to
one pair of values for

w and b that use a
particular cost j.

In fact, this booklet
pair of values for w and

b corresponds to this
function f of x,

which is this line you
can see on the left.

This line intersects the
vertical axis at 800 because

b equals 800 and the slope of
the line is negative 0.15,

because w equals negative 0.15.

Now, if you look at the data
points in the training set,

you may notice that this line

is not a good fit to the data.

For this function f of x,

with these values of w and b,

many of the predictions for
the value of y are quite far

from the actual target value of

y that is in the training data.

Because this line
is not a good fit,

if you look at the graph of j,

the cost of this
line is out here,

which is pretty far
from the minimum.

There's a pretty high cost
because this choice of

w and b is just not that good
a fit to the training set.

Now, let's look at

another example with a
different choice of w and b.

Now, here's another
function that

is still not a great
fit for the data,

but maybe slightly less bad.

This points here represents

the cost for this booklet pair

of w and b that
creates that line.

The value of w is equal to 0 and

the value b is about 360.

This pair of parameters
corresponds to this function,

which is a flat line,

because f of x equals
0 times x plus 360.

I hope that makes sense.

Let's look at yet
another example.

Here's one more
choice for w and b,

and with these values,

you end up with
this line f of x.

Again, not a great
fit to the data,

is actually further
away from the minimum

compared to the
previous example.

Remember that the minimum is at

the center of that
smallest ellipse.

Last example, if you look
at f of x on the left,

this looks like a pretty good
fit to the training set.

You can see on the right,

this point representing
the cost is very

close to the center of
the smaller ellipse,

it's not quite
exactly the minimum,

but it's pretty close.

For this value of w and b,

you get to this line, f of x.

You can see that if you measure

the vertical distances between

the data points and

the predicted values
on the straight line,

you'd get the error
for each data point.

The sum of squared
errors for all of

these data points
is pretty close to

the minimum possible sum of

squared errors among all
possible straight line fits.

I hope that by looking
at these figures,

you can get a better sense
of how different choices

of the parameters
affect the line f

of x and how this

corresponds to different
values for the cost j,

and hopefully you can see how

the better fit lines correspond
to points on the graph of

j that are closer to the
minimum possible cost

for this cost function
j of w and b.

In the optional lab that
follows this video,

you'll get to run

some codes and remember
all the code is given,

so you just need to hit

Shift Enter to run it
and take a look at it

and the lab will show you how

the cost function is
implemented in code.

Given a small training set

and different choices
for the parameters,

you'll be able to see
how the cost varies

depending on how well
the model fits the data.

In the optional lab,

you also can play with in

interactive console
plot. Check this out.

You can use your
mouse cursor to click

anywhere on the contour
plot and you will

see the straight line defined by

the values you chose for
the parameters w and b.

You'll see a dot up here also on

the 3D surface plot
showing the cost.

Finally, the optional
lab also has

a 3D surface plot
that you can manually

rotate and spin around using

your mouse cursor to take

a better look at what the
cost function looks like.

I hope you'll enjoy playing
with the optional lab.

Now in linear regression,

rather than having to
manually try to read

a contour plot for the
best value for w and b,

which isn't really a good
procedure and also won't work

once we get to more complex
machine learning models.

What you really want is

an efficient algorithm that
you can write in code for

automatically finding the
values of parameters w

and b they give you
the best fit line.

That minimizes the
cost function j.

There is an algorithm for doing

this called gradient descent.

This algorithm is one of

the most important algorithms
in machine learning.

Gradient descent and variations

on gradient descent
are used to train,

not just linear regression,

but some of the biggest and most

complex models in all of AI.

Let's go to the next
video to dive into

this really important algorithm
called gradient descent.