Maximum gradient

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.

It's on very steep ground.

What is his method going to be?

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

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

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

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

And essentially, the apartments cover the parking.

How can we describe this mathematically?

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In B, it's about zero.

Adapt maximum gradient

How can we optimize these two terms over here?

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

So at any point, the gradient is a vector.

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

The gradient with respect to W0 is very similar.

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

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.

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.

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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.

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

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

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.

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

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

It is able to move around its environment.

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

Now you propose yet another dirtbanked terminus dam with slopes of 21 2 to 1,

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

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.

When I reduce, I will do this for the one dimensional case on paper.

Is it linear or nonlinear?

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

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

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

And if you run gradient descent on a cost function like this, then gradient descent, you can show mathematically, you can find a much more direct path to the global minimum rather than taking a much more convoluted path where you're sort of trying to follow a much more complicated trajectory to get to the global minimum.

So, let's see how gradient descent works.