2.14 In this exercise, we generalize the notion of noise to the case of an arbitrary loss function L: Y  Y ! R+.

(a) Justify the following denition of the noise at point x 2 X:

noise(x) = min y02Y Ey

[L(y; y0)jx]:

What is the value of noise(x) in a deterministic scenario? Does the denition match the one given in this chapter for binary classication?

(b) Show that the average noise coincides with the Bayes error (minimum loss achieved by a measurable function).