Medium

Weighted Gini After Split

Medium

~15 min

code completion

Weighted Gini After a Split

Decision trees choose the split that most reduces impurity. After splitting a node into left and right children, the weighted Gini is:

G_{split} = \frac{n _{L}}{n} G_{L} + \frac{n _{R}}{n} G_{R}

where $n_{L}$ , $n_{R}$ are the child sizes and $n = n_{L} + n_{R}$ .

The information gain (impurity reduction) is then:

IG = G_{parent} - G_{split}

Higher information gain → better split.

Your task:

Implement weighted_gini(left_counts, right_counts) that returns the weighted Gini of the two children (not the information gain).

Example Tests

Both pure: weighted Gini = 0

Input: {"left_counts":[5,0],"right_counts":[0,5]}

Expected: 0

Both 50/50: weighted Gini = 0.5

Input: {"left_counts":[2,2],"right_counts":[3,3]}

Expected: 0.5

Larger pure child dominates

Input: {"left_counts":[8,0],"right_counts":[1,1]}

Expected: 0.1

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