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-   Chapter 4 - Overfitting (http://book.caltech.edu/bookforum/forumdisplay.php?f=111)

 ghbcode 10-10-2017 10:49 AM

Exercise 4.3

The only posting for Chapter 4 that touched on this topic is listed below though it did not explicitly cover exercise 4.3, it is somewhat touchy feely and not that exact.

Deterministic noise depends on H, as some models approximate f better
than others.
(a) Assume H is fixed and we increase the complexity of f. Will deter*ministic noise in general go up or down? Is there a higher or lower tendency to overfit?
(b) Assume f is fixed and we decrease the complexity of H. Will deter*ministic noise in general go up or down? Is there a higher or lower tendency to overfit? [Hint: There is a race between two factors that affect overfitting in opposite ways, but one wins.]

The hint to me implies the the response to a and b would move in different directions. This is what I have for an answer:
a) By increasing the target function complexity deterministic noise will increase since H remains fixed and f becomes more complex. There will be lower overfitting in the out-of-sample data. As a matter of fact this goes counter to the summary table in page 124, however, it does not make sense to me that, keeping all else constant, by increasing the target complexity we are increasing the overfit. If anything by increasing the target complexity, your fixed H would underfit.

b) By lowering the target function complexity deterministic noise would increase and there would be a tendency to lower overfit.

I'm not sure that my answer is correct so if you could enlighten me that would be most helpful. In the thread that I posted above there was discussion and use of the formula:

$E_{out}=\sigma^2+bias+var$

Question 1:
In this exercise do we assume that E_out remains fixed so that the expression is tweaked by changing H or f?

Question 2:
In part a) if you keep H fixed and increase f, what happens to deterministic noise and what happens to overfit?

Question 3:
In part b) if you keep f fixed and decrease H, what happens to deterministic noise and what happens to overfit?

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