LFD Book Forum Clarification Requested On High-N VC Bound Formula
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#1
08-05-2012, 11:28 AM
 munchkin Member Join Date: Jul 2012 Posts: 38
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.
#2
08-05-2012, 02:19 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Clarification Requested On High-N VC Bound Formula

Quote:
 Originally Posted by munchkin 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 , not for the whole bound that involves the growth function among other terms.
.
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#3
08-05-2012, 04:30 PM
 munchkin Member Join Date: Jul 2012 Posts: 38
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?
#4
08-05-2012, 09:03 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Clarification Requested On High-N VC Bound Formula

Quote:
 Originally Posted by munchkin 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.
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#5
10-24-2012, 12:48 PM
 BaLi4 Junior Member Join Date: Sep 2012 Location: Italy Posts: 2
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.
#6
10-24-2012, 04:01 PM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,478
Re: Clarification Requested On High-N VC Bound Formula

Quote:
 Originally Posted by BaLi4 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 .
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