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Old 07-10-2014, 02:53 AM
rabbitdoll rabbitdoll is offline
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Default Out of sample error for linear noisy target

I am confused about how to derive the Eout=(1+(d+1)/N)\sigma^2 for the learning curve of linear target error, as shown as the third equation in http://work.caltech.edu/library/084.pdf ?

Could anybody help me?

Thanks!
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Old 07-10-2014, 06:24 AM
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yaser yaser is offline
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Default Re: Out of sample error for linear noisy target

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Originally Posted by rabbitdoll View Post
I am confused about how to derive the Eout=(1+(d+1)/N)\sigma^2 for the learning curve of linear target error, as shown as the third equation in http://work.caltech.edu/library/084.pdf ?

Could anybody help me?

Thanks!
The derivation (sketched in Exercise 3.4 in the book) makes idealized assumptions to make it possible to get this result exactly and not asymptotically. The key assumption is that the test set inputs are the same as the training set inputs. This obviously wouldn't make sense under normal circumstances, except that in this case the "novelty" in the test set is that the noise realization is different from that of the training set. If you accept that, then the derivation would be fairly straightforward by going through the steps in the exercise.
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