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Before we start, I would like to make a very exciting announcement.

This course is so popular that we have about way more than 40 applications for our examination.

More than 40 people registered, which would make it quite likely or would require us to do a written examination in this lecture.

I guess most of you don't like that and you were thinking that this would be an oral examination.

We are trying to do an exception.

We applied officially with the Prüfungsausschuss to get the exception to do an oral examination.

But we have to see if this is actually granted, if we can actually do that.

So it may occur that we have a written examination at the end of the semester.

But we are trying to make every examination oral, because we feel it would be kind of unfair to announce a written examination right in the middle of the lecture term.

So let's see how this works out.

I ask in person if such exceptions can be granted and how likely that is.

And it seems we can get through with it.

But we have to wait until we get official feedback from the Prüfungsausschuss.

All the applications for that exception are filed.

So we submitted it, wrote an official letter, but we have to see how things work out.

You can also regard this when you're evaluating this course.

We've been doing all these substitutions and the professor wasn't there.

And then there were other guys talking about his stuff in the lecture.

But we are really trying to fight for you that we can get an oral examination, because this will be way more comfortable for you.

The written examination would, of course, be more comfortable for us.

So I try to keep this course popular, or we try to keep this course popular.

Any comments about that?

Like, thank you.

OK, so welcome back to pattern recognition.

Stefan Steidl, who gave the lecture last week, promised that Joachim Honegger will be back today.

And as you can see, he isn't.

So he has duties as the vice president of our university.

So he can't give the lecture today and he won't give the lecture tomorrow.

Tomorrow Stefan Steidl will give the lecture again.

So this is, well, we will deal with it and I hope I can meet your expectations in giving this lecture.

Last time you've been discussing primal and dual problems.

There were a couple of questions.

And now I would like to recapulate, so just rethink what we've been learning about in the case of support vector machines.

And you have seen that this is the Lagrangian function for the heart problem, where we have, where we minimize here basically the square norm of the vector alpha.

And we regularize or we add some constraints with Lagrange multipliers lambda i.

And these Lagrange multipliers enforce that we actually can separate the classes.

So you have seen that if you think about that and if you use the KKT conditions, that you can actually reformulate the problem.

And in the end you end up in a problem where you don't have alpha in there anymore.

So we replaced everything here in alpha.

And now this is where we actually can talk of the dual problem.

So we have the primal problem here and we have the dual problem here.

And in the dual problem we kicked out alpha because alpha can be described as a combination of our feature vectors and the Lagrange multipliers.

So this is what we're doing here, right?

And now there were some questions. Why can't we just solve the primal problem?

Well, you can actually solve the primal problem.

But think about it or you can do it.

You use a library and we're good.

But if you think about it, you will see your primal problem has more parameters.

Do you see that?