B is going to be his next position so this is how the hill climber decides where to go next.

In B, it's about zero.

Maximum gradient

We already know that this has a closed form solution, but just for the fun of it, let's look at gradient descent.

Now, they tell us what the slope of this line is.

How can we optimize these two terms over here?

Draw scrollbar bevel

And essentially, the apartments cover the parking.

That's where this occasion comes from in our update step. This would be simultaneous update.

Align Vertical Distribute

Align Horizontal Distribute

It sends out that at local optimum your derivative would be equal to zero.

Sixpercent grade, fast greens, breaks to the left.

How can we describe this mathematically?

So at any point, the gradient is a vector.

Now, my derivative term, d, d theta one j of theta one, when evaluated at this point, gonna look at right.

That's where the derivative is.

And it turns out there are sometimes other versions of gradient descent that are not batch versions but instead do not look at the entire traning set but look at small subsets of the training sets at the time, and we'll talk about those versions later in this course as well.

So at this point, which maybe corresponds to somewhere down here on the hill, the hill is quite steep, so our vector is quite long, and it points directly uphill.

And, you notice that my line changed a little bit.

The gradient of L with respect to W1 is minus 2, sum of all J of the difference as before but without the square times Xj.

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

But for now, using the algorithm you just learned, now we're using batch gradient descent, you now know how to implement gradient descent, or linear regression.

Adapt maximum gradient

So if you apply the rule over here, if you were to start at A as your W zero, then your gradient is negative.

And, but in case you have heard of that method, it turns out gradient descent will scale better to larger data sets than that normal equals method and, now that we know about gradient descent, we'll be able to use it in

The road across the mountain was narrow, and what's more, it was a steep slope.

It makes sense because it's a downward sloping line, but it's not too steep.

The gradient with respect to W0 is very similar.

Here is a prototypical loss function and the method for interation will be called gradient descent.

It is able to move around its environment.

It's on very steep ground.

You do this until you find yourself with what's called a local minimum, where B resides.

We create mountains of waste.

And these expressions look nasty, but what it really means is we subtract an expression like this every time we do gradient descent from W1 and an expression like this every time we do gradient descent from W0, which is easy to implement, and that implements gradient descent.

Is it linear or nonlinear?

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

It's actually a stand up product from Switzerland, because in Switzerland they have a natural need for diagonal elevators.

In this video, let's talk about how to fit the parameters of that hypothesis.

In this video, we're going to put together gradient descent with our cost function, and that will give us an algorithm for

Later in this course we will talk about that method as well that just solves for the minimum cost function J without needing this multiple steps of gradient descent.

We talked about the gradient magnitude kernel, which was defined over a square root of the squares of the image gradients.

For those of you who looked at Wikipedia to try to understand what's going on with gradient descent, the first formula you would have encountered was this one.

I find this really interesting because we can now devise a single, linear kernel that does both smoothing and find gradients at the same time.

So, this is what we worked out in the previous videos.