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Old 07-12-2012, 09:12 PM
ESRogs ESRogs is offline
Join Date: Jul 2012
Posts: 12
Default Hoeffding's inequality with M


I'm wondering why in Lecture 2 -- when we're trying to modify the right hand side of Hoeffding's inequality to take into account drawing from multiple bins (see page 16 of the slides) -- we sum all the probabilities of samples being non-representative, rather than taking 1 - the product of all the probabilities of each sample being representative.

In other words, (calling the right hand side of the original inequality p for simplicity) why doesn't the right hand side of the modified form become 1-(1-p)^M instead of M*p.

Wouldn't that be a still correct but tighter bound?

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