#5
04-08-2012, 04:01 PM
 htlin NTU Join Date: Aug 2009 Location: Taipei, Taiwan Posts: 601

Quote:
 Originally Posted by canon1230 Does the Hoeffding Inequality allow us to say something about this probability? P[|Ein - Eout| > epsilon] <= 2e^(-2 * epslion^2 * N) Since Ein = 0, N = 10, setting epsilon to 0.5, the inequality gives us: P[Eout > 0.5] <= 2e^(-5) = 0.013+ This seems to be saying something nontrivial about Eout.
The in Hoeffding is subject to the process of generating the sample (i.e. ), not the probability on . Indeed it tells us something nontrivial (and that's how we use it in the learning context), but it does not answer your original question.

The question that got answered by Hoeffding is roughly

"What is the probability of a big-Eout urn (many red) for generating such an Ein (all green)?"

not

"What is the probability of Eout being small in the first place?"

The answer to the latter question remains unknown, but even so, we know that having a big Eout is unlikely because of Hoeffding.

Hope this helps.
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