1.2 Machine learning lecture 3  (Page 14/14)

Student: [Inaudible] constants?

Instructor (Andrew Ng) :Say that again.

Student: [Inaudible]

Instructor (Andrew Ng) :Oh, right. Okay, cool.

Student: It’s the lowest it –

Instructor (Andrew Ng) :No, exactly. Right. So zero to the same, this is not the same, right? And the reason is, in logistic regression this is different from before, right? The definition of this H subscript theta of XI is not the same as the definition I was using in the previous lecture. And in particular this is no longer theta transpose XI. This is not a linear function anymore. This is a logistic function of theta transpose XI. Okay? So even though this looks cosmetically similar, even though this is similar on the surface, to the Bastrian descent rule I derived last time for least squares regression this is actually a totally different learning algorithm. Okay? And it turns out that there’s actually no coincidence that you ended up with the same learning rule. We’ll actually talk a bit more about this later when we talk about generalized linear models. But this is one of the most elegant generalized learning models that we’ll see later. That even though we’re using a different model, you actually ended up with what looks like the same learning algorithm and it’s actually no coincidence. Cool.

One last comment as part of a sort of learning process, over here I said I take the derivatives and I ended up with this line. I didn’t want to make you sit through a long algebraic derivation, but later today or later this week, please, do go home and look at our lecture notes, where I wrote out the entirety of this derivation in full, and make sure you can follow every single step of how we take partial derivatives of this log likelihood to get this formula over here. Okay? By the way, for those who are interested in seriously masking machine learning material, when you go home and look at the lecture notes it will actually be very easy for most of you to look through the lecture notes and read through every line and go yep, that makes sense, that makes sense, that makes sense, and, sort of, say cool. I see how you get this line. You want to make sure you really understand the material. My concrete suggestion to you would be to you to go home, read through the lecture notes, check every line, and then to cover up the derivation and see if you can derive this example, right? So in general, that’s usually good advice for studying technical material like machine learning. Which is if you work through a proof and you think you understood every line, the way to make sure you really understood it is to cover it up and see if you can rederive the entire thing itself. This is actually a great way because I did this a lot when I was trying to study various pieces of machine learning theory and various proofs. And this is actually a great way to study because cover up the derivations and see if you can do it yourself without looking at the original derivation. All right.

I probably won’t get to Newton’s Method today. I just want to say – take one quick digression to talk about one more algorithm, which was the discussion sort of alluding to this earlier, which is the perceptron algorithm, right? So I’m not gonna say a whole lot about the perceptron algorithm, but this is something that we’ll come back to later. Later this quarter we’ll talk about learning theory. So in logistic regression we said that G of Z are, sort of, my hypothesis output values that were low numbers between zero and one. The question is what if you want to force G of Z to up the value to either zero one? So the perceptron algorithm defines G of Z to be this. So the picture is – or the cartoon is, rather than this sigmoid function. E of Z now looks like this step function that you were asking about earlier. In saying this before, we can use H subscript theta of X equals G of theta transpose X. Okay? So this is actually – everything is exactly the same as before, except that G of Z is now the step function. It turns out there’s this learning called the perceptron learning rule that’s actually even the same as the classic gradient ascent for logistic regression. And the learning rule is given by this. Okay? So it looks just like the classic gradient ascent rule for logistic regression. So this is very different flavor of algorithm than least squares regression and logistic regression, and, in particular, because it outputs only values are either zero or one it turns out it’s very difficult to endow this algorithm with probabilistic semantics. And this is, again, even though – oh, excuse me. Right there. Okay. And even though this learning rule looks, again, looks cosmetically very similar to what we have in logistics regression this is actually a very different type of learning rule than the others that were seen in this class. So because this is such a simple learning algorithm, right? It just computes theta transpose X and then you threshold and then your output is zero or one. This is – right. So these are a simpler algorithm than logistic regression, I think. When we talk about learning theory later in this class, the simplicity of this algorithm will let us come back and use it as a building block. Okay? But that’s all I want to say about this algorithm for now.

Just for fun, the last thing I’ll do today is show you a historical video with – that talks about the perceptron algorithm. This particular video comes from a video series titled The Machine that Changed The World and was produced WGBH Television in cooperation with the BBC, British Broadcasting Corporation, and it aired on PBS a few years ago. This shows you what machine learning used to be like. It’s a fun clip on perceptron algorithm.

In the 1950’s and 60’s scientists built a few working perceptrons, as these artificial brains were called. He’s using it to explore the mysterious problem of how the brain learns. This perceptron is being trained to recognize the difference between males and females. It is something that all of us can do easily, but few of us can explain how. To get a computer to do this it would involve working out many complex rules about faces and writing a computer program, but this perceptron was simply given lots and lots of examples, including some with unusual hairstyles. But when it comes to a beetle the computer looks at facial features and hair outline and takes longer to learn what it’s told by Dr. Taylor. Andrew puts on his wig also causes a little part searching. After training on lots of examples, it’s given new faces it has never seen and is able to successfully distinguish male from female. It has learned.

All right. Isn’t that great? Okay. That’s it for today. I’ll see you guys at the next lecture.

[End of Audio]

Duration: 75 minutes