Time to record via zoom. I hope this will work.

And then I guess we can start.

Okay our topic of today is support vector regression. And for that it's good to recap the

last exercise we had just before Christmas. So if you haven't watched it yet it should be on

FIU TV and what we did there was a theory about that before our last programming exercise. So

regression is about predicting real numbers. So as a classification you get a feature vector,

we call it feature vector X. And in our example we only had one dimensional feature vector.

And what our regression task was was if we get a new point X we are supposed to predict from this

point X a real number and our prediction is as always Y. So in this example also Y would

be a real number. So X is real and also Y is real. But in theory we could also do the same

algorithm principle also to predict from a feature vector also like a prediction vector if we want

to. We can use the same algorithms. And what we did last time we had a so if we want to predict

something we actually need something that a function that is able to predict something. So

this function we called f of X and the task of this function is to predict a Y. And the other

question is how can we get this f? And for that we use our training data. Training data is always

like in our case labeled. So it's always a point A where we both know the X and the Y coordinate.

And what we do first before we can predict something for the future is we try to find a

model that kind of best explains this data here. And yeah we can use any model that we want to but

we kind of need to formulate which model would be a good one. And last time we used for this purpose

the distance. So this line here would be oops my tablet is going a bit crazy. So this is our model

f of X and this is our data. And to determine whether a model is good we kind of measure like

the difference between like our actual data and the prediction of our model in our training data.

And we do this for each and every training point, get some distances, use a function that maps our

distance to a real number. For simplicity I used here the Altoono. And then we just sum up all these

distances and the higher the distance the sum of these distances is the worse our model is. And we

kind of try to find some parameters that kind of minimize this error measure here. This was our

problem the last time. So we had linear classification, we had linear regression. And for the same

stuff you can also have like you can use support vectors. So in the lecture you did support vector

machines which would be about having two classes. So some red points and some blue points. So data

points from different classes. And you could do linear classification to fit a line that separates

those classes as well. But in support vector machine your task was basically to not only find

a line but also like a line with some epsilon kind of where you try to find like a range where

there are no data points inside. And so you would measure like the quality of your model by whether

like your points are outside of this band here. And this would be a model for classification.

And what we will do right now is, well it can fit a line so we maybe can also use this for

regression. But for classification we want to use this line to separate the points. But for

regression we actually want that all our points are within our band. And I should maybe fix my

drawing a bit. Because, no it's okay. If you have questions I cannot see the chat right now.

Please ask them loudly if it's possible. Maybe try to pause at some point to look at the chat.

But I think it's better when you just ask loudly. So chat is nothing. Okay then let's go on. Okay

like in the previous example we just measured all the errors here and added them up. And the

higher the sum of the errors was the worse our model was. And the smaller these errors were the

better our model was. And what we try to measure right now is, our goal is, this is again our model.

So this line here, model f of x. And what we try to do now is we want that all our training samples

are within an epsilon band. So we choose this epsilon. So this is our choice. Because we want

to do actually like soft support vector regression. So it should be okay for some points to be outside.

But it should be as few as possible. And the question is now how do we measure our loss? And

the idea here is that we measure now not the distance to our model. Because like everything

in this band should be okay. What we will do instead is we will measure. Like we will not only

have like a model we will also have like an upper bound f of x plus epsilon. And we will also have