Thread: Discussion of the VC proof View Single Post
#20
10-26-2016, 02:38 PM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 597
Re: Discussion of the VC proof

Suppose

Then, .

In which case and the bound in Theorem A.1 is trivial.

Quote:
 Originally Posted by CountVonCount Hi, I have a question about the sentence on page 190: While I understand the argument here, I don't understand, why it is especially the value 1/4? When set the above term to 1/4 I will receive -2*ln(1/4) as value for N*eps^2. Now I can set N*eps^2 to that value in Theorem A.1 and I will get on the RHS (assuming the growth function is just 1) 4*0,707... so it is much more than 1. A value of 1 in the RHS would be sufficient to say the bound in Theorem A.1 is trivially true. And this would assume, that the above term is less than 1/256. With this in mind 1 - 2*e^(-0.5*N*eps^2) is greater than 0,99... and thus instead of a 2 in the lemmas outcome, I would receive a value around 1, which is a much better outcome. So why is the value 1/4 chosen for the assumption? Best regards, André
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