[MUSIK]

so good morning good morning everybody to our Tuesday

morning session unfortunately yesterday I was not able to to teach but Thomas Köhler explained

to you the core idea of maximum likelihood estimation where you basically

set up a likelihood function or a log likelihood function and then

you maximize the log likelihood function in terms of the parameters that

we are looking for and we will see this over and over again

during the lecture so you will more or less grow into this

concept so what is pattern recognition in winter semester about let's look

again at the big picture to make you aware of the topics we are discussing to

make you aware of the storyline of the whole lecture so we started out basically with the motivation

of the problems we are considering we talked about basically the intention to

compute the mapping from feature vectors feature vectors to

class numbers class numbers that's basically what we discussed this semester

how can I transform feature vectors computed out of a signal

into class numbers we also know that this whole mapping is

called classification we also know if Y is a continuous parameter

a real valued number then we have a regression problem so classification and regression

are the topics we we will discuss in detail and then we looked into the concept of Bayesian

classifiers which tells us how much loss is generated by

a misclassification of a class of an object or a feature vector belonging to

class Y and being assigned to class y-prime so that's basically the

loss function is defined by loss Y y-prime and

these are the costs that I generate if an object or a pattern belonging

to class y-prime is assigned to class 1 and we have looked into a very concrete loss

function that was the so called 0 1 loss function

the 0 1 loss function is saying correct classifications are for free wrong classifications costs

1 euro 1 dollar or whatever 1 unit and if you use this cost function

then you end up with a decision rule that is optimal with respect to

the loss function in a statistical framework and that's the so called Bayesian classifier

the Bayesian classifier is optimal with respect to the 0 1

loss function if I have the posterior probabilities for all the

classes and all for the classes given the feature vector than I can build

an optimal classifier that minimizes the average loss of this

classifier and the decision rule the Bayesian decision rule is saying

we decide for the class Y star that's the optimal

class by computing argmax that's the argument for which the

posterior is maximized that's the Bayesian decision

rule we decide we compute the posteriors and at the end of the day will decide for the

class with the highest posterior that decision guarantees that we minimize the

average loss using the 0 1 loss function very cool later we will discuss other

loss functions even today will see a different loss function based on these loss functions of

course you get different different classifiers so since the mid of the sixties 1960s pattern

recognition researchers are basically looking for techniques to

find the a posterior probability because they know from a theoretical

point of view there is nothing better than that and we have seen two ways to compute it

one is the direct way that we model the posterior probability

right away these are the so called discriminative models

discriminative approach where we compute P of YX right

away and the generative model makes use of the Bayesian formula which