So here's our cost function.

Now, let's define the cost function for our cost function for our neural network.

And so we'll implement this Path Cost function, in terms of a Step Cost function.

Okay. So that's the cost function.

Thus minimizing that cost function j.

Using this simplified definition of a hypothesizing cost function let's try to understand the cost function concept better.

We do this by minimizing the cost function.

The first is the hypothesis function, and the second is a cost function.

But, it turns out that the cost function for gradient of cost function for linear regression is always going to be a bow shaped function like this.

Just write this out, this is my cost function.

Usually, we're given some sort of a cost function.

And notice, because my cost function is a function of my parameter theta one, when I plot my cost function, the horizontal axis is now labeled with theta one.

As usual, here are plots of the hypothesis function and of my cost function J.

In this video we'll define something called the cost function.

Octave, I run j equals cost function j x y theta.

The, the square cost function that we came up with earlier.

Maybe it's a cost function from linear regression. Maybe it's some other function we want to minimize.

K equals one through four of basically the logistic regression algorithms cost function but summing that cost function over each of my four output units in turn.

look at an example. So here's a cost function J with theta.

Here is the cost function j of theta that we have for

Here's the cost function that we wrote down in the previous video.

So there has to be function, the function has to be predictable and the cost has to be low.

So, this cost function is also called the squared error function or sometimes called the square error cost function and it turns out that Why, why do we, you know, take the squares of the errors?

If you look at the cost function of logistic regression, what you find is that each example x, y, contributes a term like this to the overall cost function.

This is cost 0 of theta transpose x where the cost 1 function is what we had on the previous

In the previous video, we gave the mathematical definition of the cost function.

And I have also moved to a new point on my cost function.

So, that's the gradient descent algorithm, and you can use it to minimize, to try to minimize any cost function J. Not the cost function J to be defined for

So that is going to be one over 2M of, my usual cost function.

Here's my cost function for the support vector machine where here on the left

This function on the left, I'm going to call cost subscript 1 of z.

In the previous video, we talked about a cost function for the neural network.

You have to have low cost, but you also have to have a function.

In the next video, we're going to take the function J, and set that back to be exactly linear regression's cost function.

So let's go ahead and compute what the cost function has for. You'll devalue one.

And this function on the right, I'm going to call cost subscript 0 of z.

For a neural network our cost function is going to be a generalization of this.

So, that's the cost function we're going to use to fill on your own network.

And this hypothesis again has some cost, and that cost is, you know, plotted as the height of the J function at that point.

X. In contrast, the cost function, J, that's a function of the parameter, theta one, which controls the slope of the straight line.

Here at my desktop, I've predefined does cost function j and if I bring up the definition of that function it looks as follows.

Let's plot that. What I'm gonna do on the right is plot my cost function j.

Here's our problem formulation as usual, with the hypothesis parameters, cost function, and our optimization objective.

The question now is optimal alignment of the top to the bottom under this cost function?

What we're going to do is apply gradient descent to minimize our squared error cost function.