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-   -   Clarification Requested On High-N VC Bound Formula (http://book.caltech.edu/bookforum/showthread.php?t=949)

munchkin 08-05-2012 12:28 PM

Clarification Requested On High-N VC Bound Formula
 
The instructions at the top of the assignment specify in problems 1 to 3 that for N > Dvc the growth function should be defined as N raised to the Dvc power.

As I understand it that statement directs me to substitute the formula above anywhere the growth function is used in problems 1 to 3 regardless of the dependency on N actually displayed in the problem -- 2N and N^2 factors are to be ignored.

Am I mistaken in this interpretation? Thanks for your attention.

yaser 08-05-2012 03:19 PM

Re: Clarification Requested On High-N VC Bound Formula
 
Quote:

Originally Posted by munchkin (Post 3810)
The instructions at the top of the assignment specify in problems 1 to 3 that for N > Dvc the growth function should be defined as N raised to the Dvc power.

As I understand it that statement directs me to substitute the formula above anywhere the growth function is used in problems 1 to 3 regardless of the dependency on N actually displayed in the problem -- 2N and N^2 factors are to be ignored.

Am I mistaken in this interpretation? Thanks for your attention.

The formula is for the growth function m_{\cal H} (), not for the whole bound that involves the growth function among other terms.
.

munchkin 08-05-2012 05:30 PM

Re: Clarification Requested On High-N VC Bound Formula
 
Thanks for the quick response.

So for the case N > Dvc, within any of the formulas that define the various bounds, where there is a growth function reference it should be replaced by N raised to the power Dvc?

yaser 08-05-2012 10:03 PM

Re: Clarification Requested On High-N VC Bound Formula
 
Quote:

Originally Posted by munchkin (Post 3815)
Thanks for the quick response.

So for the case N > Dvc, within any of the formulas that define the various bounds, where there is a growth function reference it should be replaced by N raised to the power Dvc?

Correct. The simplification is meant to make the answer independent of the different bounds that can be used.

BaLi4 10-24-2012 01:48 PM

Re: Clarification Requested On High-N VC Bound Formula
 
I'm a bit confused by the answer. Before reading the post, I was quite sure about substituting m_{\cal H}(2N) with (2N)^{d_{vc}}, not with (N)^{d_{vc}} for N>d_{vc}. Could you please confirm the former is the correct approximation of the growth function when the argument is 2N? Thank You.

yaser 10-24-2012 05:01 PM

Re: Clarification Requested On High-N VC Bound Formula
 
Quote:

Originally Posted by BaLi4 (Post 6939)
I'm a bit confused by the answer. Before reading the post, I was quite sure about substituting m_{\cal H}(2N) with (2N)^{d_{vc}}, not with (N)^{d_{vc}} for N>d_{vc}. Could you please confirm the former is the correct approximation of the growth function when the argument is 2N? Thank You.

Confirmed. It is (whatever the argument of the growth function is) raised to the power d_{\rm vc}.


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