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Old 10-05-2016, 03:23 PM
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htlin htlin is offline
Join Date: Aug 2009
Location: Taipei, Taiwan
Posts: 610
Default Re: Discussion of the VC proof

Originally Posted by CharlesL View Post
Recently I have started reading the proof of the VC inequality in the appendix. On the bottom of page 190(Lemma A.3) , why does

sigma_S P[S] x P[sup_h E_in - E_in' > ... |S ] <= sup_S P[sup_h E_in - E_in' >...|S ]?
(Sorry for the terrible notations, I don't know how I can input math symbols)

what does it mean by taking the supremum on S?
All complicated math aside, supremum on S carries the physical meaning of taking the "maximum" value over all possible S.

So this inequality simply says an expected value (of P[sup_...]) is less than or equal to the maximum value.

Hope this helps.
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