[MUSIK]

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of Erlangen Nürnberg so it's 1 plus D then it's D minus

1 plus 2 so D minus 1 plus 2 so

it's again D plus 1 plus and how often do we need that D times

right we have D times over 2 so we have D

plus one half so that's the number of degrees of freedom so

that's a huge number if we have 100 dimensional features then you can find out

that you need tons of parameters that you have to estimate out of the training data and

and one idea you got that that was the idea of little Gauss third year at school

or something like that you remember the famous story when the teacher of Gauss

came to school after carnival was still a little bit with alcohol in blood

and then he said okay can you please sum up all the numbers from

1 to 1000 and then he wanted to have a nice day and Gauss

came with a solution after three minutes you don't remember that that's the

story it's coming back over and over again not the alcohol in the blood but the story

and the problem itself which tells us it the for me that's always a nice example if I go to school and

explain people or to students potential students what computer science is and why

it's important that you know how to think about problems okay you know about

the second nice problem I always explain to students to check whether your are

able to study computer science now you are filming right I'll tell

you by the way it's nice it's nice can you imagine that's a glass of red wine so it's

red wine and this is a white wine it has nothing to do

with Unix and read and writer permissions red wine and white wine red wine

and white wine and the question you take a spoon of the red wine and put it into the

white wine and then you your mix things up and then you take the spoon and do one spoon

back into the red wine and the question is is there more red wine in the

white wine or more white wine in the white wine more white wine in the red wine and

it's a very nice problem and I explain it to students this way computer

scientists think the following way think about a spoon that is

very very small so it cannot even carry one molecule right think about a spoon

that cannot carry even one molecule what happens you bring it over you mix

it you bring it back so it's it's the same ratio right and now

take a spoon that is twice as large as one of the glasses here

so you put the whole glass in you put it in here you mix

it and then put back half a glass sorry that is exactly the spoon

should have exactly the size of the glass so you take the whole glass in here you mix

it and then you bring half back so the ratio is still the same why should

it different be different in between right that's the argument okay why should it be different

in between that's a legal argument but it's not pattern recognition

so forget about this okay but it's

the the way of of thinking that we expect from our students right

so how do we break down the number of parameters and now we are in the middle of the topics

we have considered last week we were assuming that these elements

here of the feature vector are mutually independent and that's

a standard trick in pattern recognition if the problem itself grows in

terms of its dimensionality usually we start to assume independence

assumptions or we start to bring in independence assumptions and

one was to say okay the components of X are

mutually independent independent so that's basically P of X given Y