[gjtucker]

It seems like it depends on the definition of deterministic noise. If we define it as E_x[(g^{bar}(x) - f(x))^2] (as was done in the lecture slides) and we assume that g^{bar} is the best hypothesis in H, then it is independent of N.

Where the finite N comes in is through the variance term. With few N, the more complicated model will have a harder time finding the best hypothesis and have high variance, which what we see in the plots in lecture. But, as N increases, my guess is that E_x[(g^{bar}(x) - f(x))^2] says approximately the same, while the variance term goes down. I suppose this wouldn't be too hard to check numerically.