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Old 04-17-2013, 08:31 AM
matthijs matthijs is offline
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Default The role of noise

I'm having trouble understanding the role of noise. The generalization bound depends on N, the VC dimension of H, and delta.

I notice that in later lecture slides, noise forms an explicit term in the bias-variance decomposition, i.e. more noise increases the expected E_out (apologies for referring to slides that haven't been discussed yet).

Why doesn't it feature in the generalization bound? Is it because it is captured in the E_in term, i.e. more noise will increase our training error? In earlier lectures, N was written in terms of the growth function, to see how much data we need; and a rule of thumb was given that says N >= 10*VCdim. I'd like understand quantitatively how our need for data grows with noise, but I don't see how to do this using the generalization bound or bias-variance.
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Old 04-17-2013, 11:21 AM
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yaser yaser is offline
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Default Re: The role of noise

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Originally Posted by matthijs View Post
I'm having trouble understanding the role of noise. The generalization bound depends on N, the VC dimension of H, and delta.

I notice that in later lecture slides, noise forms an explicit term in the bias-variance decomposition, i.e. more noise increases the expected E_out (apologies for referring to slides that haven't been discussed yet).

Why doesn't it feature in the generalization bound? Is it because it is captured in the E_in term, i.e. more noise will increase our training error?
Your understanding is correct. Noise increases both E_{\rm in} and E_{\rm out}. Generalization error is the difference between the two. The more critical impact of noise, that of overfitting, will be discussed in Lecture 11.
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