Easy

Gini Impurity

Easy

~12 min

code completion

Gini Impurity

Gini impurity measures how often a randomly chosen element would be misclassified if randomly labeled according to the class distribution. It's used by CART decision trees to choose split points.

G = 1 - k = 1 \sum K p_{k}^{2}

where $p_{k}$ is the proportion of class $k$ in the node.

Properties:

G = 0

: perfectly pure node (all one class)

G = 0.5

: maximally impure binary node (50/50 split)

Your task:

Implement gini_impurity(counts) where counts is an array of class counts (not probabilities). Convert to proportions first.

Example Tests

Pure node: Gini = 0

Input: {"counts":[10,0]}

Expected: 0

50/50 binary split: Gini = 0.5

Input: {"counts":[5,5]}

Expected: 0.5

3/1 split: Gini = 0.375

Input: {"counts":[3,1]}

Expected: 0.375

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