1.1 Machine learning lecture 2  (Page 11/15)

Oh, and as usual, this is really – you update all the parameters data runs. You perform this update for all values of I. For I indexes and the parameter vectors, you just perform this update, all of your parameters simultaneously. And the advantage of this algorithm is that in order to start learning, in order to start modifying the parameters, you only need to look at your first training examples.

You should look at your first training example and perform an update using the derivative of the error with respect to just your first training example, and then you look at your second training example and perform another update. And you sort of keep adapting your parameters much more quickly without needing to scan over your entire U.S. Census database before you can even start adapting parameters.

So let's see, for launch data sets, so constantly gradient descent is often much faster, and what happens is that constant gradient descent is that it won't actually converge to the global minimum exactly, but if these are the contours of your function, then after you run the constant gradient descent, you sort of tend to wander around.

And you may actually end up going uphill occasionally, but your parameters will sort of tender to wander to the region closest to the global minimum, but sort of keep wandering around a little bit near the region of the global [inaudible]. And often that's just fine to have a parameter that wanders around a little bit the global minimum. And in practice, this often works much faster than back gradient descent, especially if you have a large training set.

Okay, I'm going to clean a couple of boards. While I do that, why don't you take a look at the equations, and after I'm done cleaning the boards, I'll ask what questions you have.

Okay, so what questions do you have about all of this?

Student: [Inaudible] is it true – are you just sort of rearranging the order that you do the computation? So do you just use the first training example and update all of the theta Is and then step, and then update with the second training example, and update all the theta Is, and then step? And is that why you get sort of this really – ?

Instructor (Andrew Ng) :Let's see, right. So I'm going to look at my first training example and then I'm going to take a step, and then I'm going to perform the second gradient descent updates using my new parameter vector that has already been modified using my first training example. And then I keep going.

Make sense? Yeah?

Student: So in each update of all the theta Is, you're only using –

Instructor (Andrew Ng) :One training example.

Student: One training example.

Student: [Inaudible]?

Instructor (Andrew Ng) :Let's see, it's definitely a [inaudible]. I believe this theory that sort of supports that as well. Yeah, the theory that supports that, the [inaudible]of theorem is, I don't remember.

Okay, cool. So in what I've done so far, I've talked about an iterative algorithm for performing this minimization in terms of J of theta. And it turns out that there's another way for this specific problem of least squares regression, of ordinary least squares. It turns out there's another way to perform this minimization of J of theta that allows you to solve for the parameters theta in close form, without needing to run an iterative algorithm.