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#1
10-20-2012, 10:32 AM
 axelrv Junior Member Join Date: Sep 2012 Posts: 6
Variance of Eval

I'm confused about how to simplify expressions involving Var[Eval(g-)].

I know that Var[Eval(g-)] = E [ ( Eval(g-) - E[Eval(g-)] )^2] = E [ ( Eval(g-) - Eout(g-) )^2] and that for classification P[g-(x) != y] = Eout(g-). I'm not sure how to bring K into any of these expressions.

Any help would be greatly appreciated.
#2
10-21-2012, 07:51 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 597
Re: Variance of Eval

Here are two useful facts from probability:

The variance of a sum of independent terms is the sum of the variances:

When you scale a random quantity its variance scales quadratically:

[Hint: so, if you scale something by its variance scales by ; the validation error is the average of K independent things (What things? Why are they independent?)]

Quote:
 Originally Posted by axelrv I'm confused about how to simplify expressions involving Var[Eval(g-)]. I know that Var[Eval(g-)] = E [ ( Eval(g-) - E[Eval(g-)] )^2] = E [ ( Eval(g-) - Eout(g-) )^2] and that for classification P[g-(x) != y] = Eout(g-). I'm not sure how to bring K into any of these expressions. Any help would be greatly appreciated.
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