LFD Book Forum (http://book.caltech.edu/bookforum/index.php)
-   Homework 4 (http://book.caltech.edu/bookforum/forumdisplay.php?f=133)
-   -   The role of noise (http://book.caltech.edu/bookforum/showthread.php?t=4216)

 matthijs 04-17-2013 08:31 AM

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.

 yaser 04-17-2013 11:21 AM

Re: The role of noise

Quote:
 Originally Posted by matthijs (Post 10455) 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 and . Generalization error is the difference between the two. The more critical impact of noise, that of overfitting, will be discussed in Lecture 11.

 All times are GMT -7. The time now is 10:22 PM.