Thread: role of P(X) ?
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Old 04-11-2013, 07:04 AM
kokrah kokrah is offline
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Join Date: Apr 2013
Posts: 3
Default Re: role of P(X) ?

I see.

Example:
Y|x = x + \epsilon is the target.
X \sim F(x) is the input space.

If we let 1. \epsilon \sim N(0,1); X \sim N(0,1)
or
2. \epsilon \sim N(0,1); X \sim t(1), where t(1) is the t-distribution 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 mis-conceptions about the theoretical framework of the learning problem once and for all
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