[MUSIK]

and I put up again one important formula where yesterday I was

not clear enough I guess in explaining this what we see here is the

average loss of a classifier once again the loss function

tells us basically how much a misclassification is and the

simplest loss function is we pay 1 euro for misclassification and

if we do the decision correctly then everything's fine and we

weighted by 0 and the average loss for a given feature

vector and a given class is given here by the sum

over the loss function multiplied with the posterior okay and if you

look at the posterior probabilities these are numbers positive numbers in

between 0 and 1 okay in between 0 and 1 and

when is this sum the smallest well we sum up

here the posteriors the posteriors are weighted by the loss

and if we decide for the class Y with the

highest a posterior probability what does that mean that we

cancel out of the sum the element with the highest a posterior

probability due to the fact that all the components are none negative

the overall sum the overall average loss is 0 if we take

out the smallest value right the highest a posteriori probability and that's

the idea the Bayesian classifier will decide for the class with

the highest a posterior probability and once again it sounds so trivial in

this audience here in the lecture the Bayesian decision rule is nothing else

but computing the posteriors for all classes given a feature vector and then

we decide for the class with the highest a posteriori probability welcome okay

good and today we are

going to continue welcome you

are late okay if you have trouble to find the

room can you imagine what kind of trouble you will have answering my questions it's always

nice to see people walking around with a GPS finding the

lecture halls you know times have changed times have changed that's

cool okay so besides all the

math today we will have a lot of technical discussions we

will massage a lot of formulas using plus minus multiplication ratio

computation so basic math but it's a lot we're going to do but keep in mind the

story we have in the background what I'm going to consider in the following and if I

consider this you will also consider this let's consider the following problem we

have a feature vector with two elements 2-D features we have a

a labeled training set so we do supervised learning so we have

features here and features here and one feature set is belonging to the

class 0 we will call it 0 and 1 and then we have in addition to

that the decision boundary and this decision boundary is usually defined

by the zero level set of a function f capital f that's usually

the zero level set that the set of all the points X

where this function ends up with a final value 0 okay and

the question we are considering is what is the a posteriori probability

for Y is 0 given X and Y is

plus 1 given X for this decision boundary defined by

this zero level set that sounds very complicated that sounds very complicated but

we will see it so if you do it the right way it's it's not not so hard so we