
#1




role of P(X) ?
The Hoeffding bound for the model H in chapter one, only requires that
we make the assumption that the input examples are a random sample from the bin; so we can generalize the sample error. What role does the distribution on X play? It appears to me that we don't need it. (at least the way the issue of feasibility is setup in chapter 1) ie. true mismatch ~ sample mismatch. Thanks. 
#2




Re: role of P(X) ?
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#3




Re: role of P(X) ?
So can you say that P(X) populates the bin and determines mu? In that case we would be sampling P(X); is this correct?

#4




Re: role of P(X) ?
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#5




Re: role of P(X) ?
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Thanks prof Yaser's reply. A quick question, as we are sampling according to , how effect each ? In other words, determines or Sampling process or both? 
#6




Re: role of P(X) ?
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#7




Re: role of P(X) ?
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But isn't fixed when you choose a particular hypothesis h. [ Because number of red marbles is equal to the number of points in the input space where hypothesis ( h ) and target function ( f ) disagree. And this, in my opinion, has nothing to do with probability distribution function ] Please clarify. Thanks, Giridhar. 
#8




Re: role of P(X) ?
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To take a simple example, Let's say that there are only two marbles in the bin, one red and one green, but the red marble has a higher probability of being picked than the green marble. In this case, is not 1/2 though the fraction of red marbles is 1/2.
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#9




Re: role of P(X) ?
I see.
Example: is the target. is the input space. If we let 1. or 2. , where t(1) is the tdistribution with one degree of freedom. I know from my stat classes that in case 1. a linear model is actually "correct". (this is great since we usually know nothing about f) So in this case the distribution of X plays a role in selecting H, and hence reducing the in sample error. (assuming the quadratic loss fct.) Questions: So in either case 1. or 2. the interpretation/computation of the sample error is the same? I am a little confused since the overall true error (which we hope the sample error approximates) is defined based on the joint distribution of (X,Y); which depends on the distribution of X. Thanks. I hope this class/book can clear up some misconceptions about the theoretical framework of the learning problem once and for all 
#10




Re: role of P(X) ?
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[This may appear to be a trivial assumption when sampling from some populations, but it is likely to be nontrivial in many cases where we are attempting to infer future behavior from past behavior in a system whose characteristics may change] 
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