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Old 02-09-2013, 10:01 PM
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yaser yaser is offline
Join Date: Aug 2009
Location: Pasadena, California, USA
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Default Re: Doubt from lecture 2(Is learning feasible?)

Originally Posted by shirin View Post
Can't I start talking about hypothesis analogy without making this assumption?

I mean if i say that a hypothesis is analogous to a bin and then I say that for any hypothesis there is a probability that that it will make a wrong classification in the bin and in the sample with probability \mu & \vu.

And then go ahead with hooeffding's inequality.

In doing so do I really need that assumption?
The introduction of a probability is not needed to make the analogy between a hypthesis and a bin, but it is needed to invoke Hoeffding inequality on the bin (and the hypothesis). Think of it this way. If I choose 3000 voters according to a deterministic criterion (say the richest 3000 people in the country) and poll them about who they are going to vote for, this sample will not indicate how the population as a whole will vote. If I introduce a probability distribution (say each voter in the population is as likely to be chosen for the poll as every other voter), then I can apply statistical results like Hoeffding to infer from a random sample of 3000 people how the population as a whole will vote.
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