Why we are using squared probabilities instead of normal probabilities in Gini impurity . Probabilities will always be positive, so why to square those?
The above answers are all excellent. When I had the same question, I managed to get an intuition of this by simply doing the following
temp=  for j in range(0, 10): i = j / 10.0 num1 = i * i num2 = (1-i) * (1-i) temp.append(num1 + num2) print(temp) temp = [1.0, 0.8200000000000001, 0.6800000000000002, 0.58, 0.52, 0.5, 0.52, 0.58, 0.6800000000000002, 0.8200000000000001]
As you can see, the sum of squares minimizes when at least one of the probabilities goes towards extreme values (0 and 1 being extremes). In Gini impurity, that is what we want - we want to split the node which results in the probabilities of 2 classes being extreme. i.e. one split should have only members of class A and another split members of class B (if this was a 2-class problem).
As you can see form the above, that is achieved when you maximize the sum of squares of probabilities.