1.6 Machine learning lecture 7  (Page 22/15)

MachineLearning-Lecture07

Instructor (Andrew Ng) :Good morning. So just a few quick announcements. One is for the SCPD students – that would be for the students taking the classes remotely – to turn in the process solutions due this Wednesday, please fax the solutions to us at – so the fax number written at the top of the Problem Set 1. And in particular, please do not use the SCPD [inaudible], since that usually takes me longer for your solutions to get to us.

And everyone else, if you're not an SCPD student, then please only turn in hard copies – the physical paper copies of your solutions from Set 1. And please don't email them to us or send them by fax unless you're an SCPD student.

Also, as you know, project proposals are due this Friday. And so in my last few office hours, you should have lively discussions with people about [inaudible] ideas.

This Wednesday, immediately after class, so this Wednesday, starting about, I guess 10:45, right after class, I'll be holding extra office hours in case any of you want to discuss project ideas some more before the proposals are due on Friday, okay?

But is this loud enough? Can people in the back hear me? Is this okay?

Student: [Inaudible] louder, maybe?

Instructor (Andrew Ng) :[Inaudible] turn up the volume, [Inaudible]? Is this okay? Testing, testing. It's better? Okay, great.

So that was it for the administrative announcements.

So welcome back. And what I wanna do today is continue our discussion on support vector machines. And in particular, I wanna talk about the optimal margin classifier. Then I wanna take a brief digression and talk about primal and duo optimization problems, and in particular, what's called the KKT conditions. And then we'll derive the duo to the optimization problem that I had posed earlier.

And that will lead us into a discussion of kernels, which I won't really – which we just get to say couple words about, but which I'll do probably only in the next lecture.

And as part of today's lecture, I'll spend some time talking about optimization problems. And in the little time I have today, I won't really be able to do this topic justice. I wanna talk about convex optimization and do that topic justice. And so at this week's discussion session, the TAs will have more time – will teach a discussion session – focus on convex optimization – sort of very beautiful and useful theory. So you want to learn more about that, listen to this Friday's discussion session.

Just to recap what we did in the previous lecture, as we were beginning on developing on support vector machines, I said that a hypothesis represented as H sub [inaudible] wb as g of w transpose [inaudible]x + b, where g will be +1 or -1, depending on whether z is greater than 0. And I said that in our development of support vector machines, we'll use – we'll change the convention of letting y be +1, -1 to note the class labels.

So last time, we also talked about the functional margin, which was this thing, gamma hat i. And so we had the intuition that the if functional margin is a large positive number, then that means that we are classifying a training example correctly and very confidently.