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

It's on very steep ground.

Maximum gradient

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

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

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

Draw scrollbar bevel

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

What is his method going to be?

And essentially, the apartments cover the parking.

Notice also that on all of these graphs, the slope is steeper on in group, authority, purity.

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.

Sixpercent grade, fast greens, breaks to the left.

But there is a very curious pattern in the rest of the 20th century, because we see a sharp decline in this Islamic modernist line.

And if you want to eye ball where is equivalence point, you look for the steepest point in the graph.

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.

In B, it's about zero.

Emergency bulkheads are engaged.

How can we describe this mathematically?

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

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

Emergency evasives.

Send an ambulance immediately. Over.

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

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.

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

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

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

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

Adapt maximum gradient

How can we optimize these two terms over here?

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.

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.

The gradient with respect to W0 is very similar.

Gibbons had heard nothing of the morning's occurrences, but the phenomenon was so striking and disturbing that his philosophical tranquillity vanished he got up hastily, and hurried down the steepness of the hill towards the village, as fast as he could go.

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.

It is able to move around its environment.

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

Finally, just to give this another name, it turns out that the algorithm that we just went over is sometimes called batch gradient descent.

B, our new location becomes yi prime.

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