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#1
11-10-2013, 03:25 PM
 Sandes Junior Member Join Date: Sep 2013 Posts: 2
Problem 5.1b

I get as far as this
P ≥ 1 - 4mH(N)^2/e^(N/32)

but I'm not certain how to go about showing that P ≥ 1 - mH(N)/2^N

Maybe I have totally the wrong approach:
I started with
Eout(h) ≤ Ein(h) + sqr (8/N ln(4mH(N)^2/δ)) with P ≥ 1-δ
So perhaps there's another formula that would work better. I feel like I'm making a silly mistake somewhere but I'm not sure what it could be.
#2
11-17-2013, 10:51 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Problem 5.1b

If the data is generated from a random (arbitrary) target function, then every dichotomy is equally likely. Since you can implement at most m(N) of these dichotomies, the number of dichotomies you cannot implement is at least 2^N-m(N). Each of these dichotomies you cannot implement has probability 1/2^N

Quote:
 Originally Posted by Sandes I get as far as this P ≥ 1 - 4mH(N)^2/e^(N/32) but I'm not certain how to go about showing that P ≥ 1 - mH(N)/2^N Maybe I have totally the wrong approach: I started with Eout(h) ≤ Ein(h) + sqr (8/N ln(4mH(N)^2/δ)) with P ≥ 1-δ So perhaps there's another formula that would work better. I feel like I'm making a silly mistake somewhere but I'm not sure what it could be.
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Have faith in probability
#3
01-07-2018, 01:50 AM
 samarhabibi Junior Member Join Date: Jan 2018 Location: Tehran Posts: 1
Re: Problem 5.1b

I just want to say thank you, my problem is solved
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