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 bigEout 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.