Chapter 8 - Tree-based methods

Question 1

Definitions of the quantities
Gini index (G)
Classification error (E)
Cross-entorpy (D)

Answer 1

G = sum_overAllK (^p _ mk(1-^p _ mk))
E = 1 - max _ k (^p _ mk)
D = - sum _ overAllK (^p _ mk(log(^p _ mk)))

K = 2:
E, 1 > ^p _ m1 > 0.5 for class 1
G = 2 ^ p_m1 (1-^p _ m1) small vales close to 0 or 1
D = - ^p _ m1 log(^p _ m1) - (1 - ^p_m1) log(^p _ mk)