Hello, welcome.

I thought it would be good to do a video on how you can solve this task here for the Gaussian

mixture classifier.

To be exact, I already did a video but without any audio.

So this is already the second time that I'm doing this.

But yeah, no, this is not important here for you.

Like basically, what is the basic story that we try to do now.

So we want to do a Gaussian mixture classifier.

So again, a classifier.

So a classifier, what it does is you get an extra feature vector and then you should tell

like which class is this.

So if you have two, three classes, so Y could be either Y1, Y2, or Y3.

And yeah, we should answer another question.

And what do we get for this task is we get a feature space.

So feature space.

And in our task our feature space is two dimensional.

But for these explanations here, I guess, yeah, it's just better to do it in one dimension.

So feature space X, X like the feature vector live on these axes.

And they have different labels.

So we know their class in our training set in advance.

We should use that knowledge to kind of develop a model so that when we get then an X label

of outer class label that we can then tell which class it is.

So assuming we have three classes, then maybe blue dots live here or here.

And we have maybe like pinkish class, pink samples live here and maybe some of them here.

And then we also have a third class and we use green for it.

So and green samples, just say the green samples live here.

Some rare green samples here.

And what our task is, is we would like to get a model for each of these class.

So one model per class task.

One generative model.

And so what we want to do now is for each class, like we have a green class, we want

to have a model for how these points are distributed here.

So we want to have a model for X, the position of X.

And we will have one model for the green class and X.

Then we will have one model for the pink class.

So this would be maybe like this.

Like, okay, this one is smaller from this here.

So this one would be bigger.

And here we only have two little samples.

So this would be, this bump here would be smaller.

And then a model for the blue class.

Okay, big bump here.

And yeah, like a middle bump here, the other blue sample.

And this would be the model for the distribution of X, given the assumption that we have the

blue class.

And then we have like a model for X, given that we have pink class.

And yeah, this axis would be, here we put our distribution for X given class Y.

So this is what we want to do now.

And this is different from what we did before, like for logistic regression.

So what we actually need for classification is we need, so we need to get this Y here.