First of all, I would like to thank you, haruspex and Andrew, for your patience. I could follow Andrew's reformulation and, as I understand it, it seems precise. Well, to understand a precise description is easier than to formulate it and I know I wasn't able to do it well when trying to shortly...
P\ [\sup\limits_{H}\ |Ein(h)\ -\ E'in(h)|\ >\ \epsilon\ |\ S] and \sup\limits_{H}\ P\ [\ |Ein(h)\ -\ E'in(h)|\ >\ \epsilon\ |\ S]
I have commited an error when changing the expression.
Yes, it is a measure of error. The whole proof has as a goal to transform Hoeffding's inequality in...
Thanks haruspex for your patience.
This is why I think I'm making some conceptual confusion. My source was a machine learning book which is used as source for an online course. I have changed some terms because it would be confusing to transcribe them literally and the proof is too long to...
I used capital X under the supremum, but didn't know if I should do it inside the function, since the notation I'm used to is to use capital letters to represent the whole set only.
I will try to make it clearer:
P\ [\sup\limits_{X}\ |f(X)\ -\ f'(X)|\ >\ 5] and \sup\limits_{X}\ P\ [\...
P\ [\sup\limits_{X}\ |f(x)\ -\ f'(x)|\ >\ y] and \sup\limits_{X}\ P\ [\ |f(x)\ -\ f'(x)|\ >\ y]
I'm sorry. That's the first time I'm posting here and the first time I'm using Latex. I'm still getting used to it.
I've got rid of z and consider y a constant; f and f' are two different...
I'm trying to deal with the supremum concept in a specific situation, but I think I'm getting the concept wrong.
A step of a proof I'm going through states:
P\ [\sup\limits_{x}\ |f(x)\ -\ f'(x)|\ >\ y\ |\ z]\ \ \leq\ \ \sum_{i=1}^M\ P\ [\ |f(x)\ -\ f'(x)|\ >\ y\ |\ z]\ \ \leq\ \ M\times\...