7.7 Noise-tolerant AdaBoost. AdaBoost may be signicantly overtting in the presence of noise, in part due to the high penalization of misclassied examples. To reduce this eect, one could use instead the following objective function:

F =

Xm i=1 G(????yif(xi)); (7.32)

where G is the function dened on R by G(x) =

(

ex if x  0 x + 1 otherwise:

(7.33)

(a) Show that the function G is convex and dierentiable.

(b) Use F and greedy coordinate descent to derive an algorithm similar to AdaBoost.

(c) Compare the reduction of the empirical error rate of this algorithm with that of AdaBoost.