Welcome to the most exciting lecture of the curriculum in computer science, technical

mathematics and whatever you are studying.

We talk about the most exciting algorithm in the field of pattern analysis and the most

exciting algorithm is beyond many other exciting algorithms, the EM algorithm.

And yesterday we started to introduce the EM algorithm that is basically nothing else

but an ML estimator, maximum likelihood estimator that reduces or transforms the maximum likelihood

estimation to an iterative maximization scheme of the so-called Q function or Kovac Leibler

statistics.

So let me insert a picture.

So we have discussed the EM algorithm.

EM stands for?

Right.

So you did the first step in the right direction.

The EM algorithm.

And the EM algorithm is working as follows.

How do you remember that?

First of all, we have two random variables, X and Y.

What is X?

What is Y?

X is the observable.

What is Y?

The hidden.

Do you know why hidden Markov models are called hidden Markov models?

It's related to that.

You will see that later on.

And then we have barometers B. Yeah?

Barometer set is called B. Parameters.

And then we have the missing information principle.

And the missing information principle is extremely difficult.

It's saying the observable information is the complete information minus the hidden

information.

That means the observable information is the complete information.

Complete.

It's complete if I have X and Y. B minus the hidden information.

So log P of Y given X and B. That's the missing information principle.

Just multiply it with minus one and then you have exactly what we know from information

theory.

And then we consider this in the i plus first iteration.

i plus first iteration.

i plus first iteration.

You remember that?

We did that yesterday.

And then we said, oh, we multiply this with P of Y given X, B in the ith iteration.

So what we do is we multiply this P Y given X, B i.

P Y given X, B i.

In the ith iteration.

P Y given X, B i.

So we have considered this in the i plus first iteration and then for some reason we multiplied

that.

And then Kirsten is telling me, what is this?