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Gini Impurity

Compute the Gini impurity of a set of labels.

Gini impurity measures how often a randomly chosen element would be incorrectly classified:

$Gini = 1 - \sum_{k=1}^{K} p_k^2$

where $p_k$ is the proportion of class $k$ in the dataset.

A pure node (all same class) has Gini = 0. Maximum impurity for binary classification is 0.5.

Return the Gini impurity rounded to 4 decimal places.

Input:

labels = [1, 1, 0, 0, 0]

Output:

0.48

Reasoning:

First, we calculate the proportion of each class in the dataset: $p_0 = \frac{3}{5}$ for class 0 and $p_1 = \frac{2}{5}$ for class 1.
Then, we apply the Gini impurity formula: $Gini = 1 - (p_0^2 + p_1^2) = 1 - (\left(\frac{3}{5}\right)^2 + \left(\frac{2}{5}\right)^2)$
The calculation yields: $Gini = 1 - \left(\frac{9}{25} + \frac{4}{25}\right) = 1 - \frac{13}{25} = \frac{12}{25} = 0.48$
The final output is the Gini impurity rounded to 4 decimal places, which is $0.4800$ , but since it's already in the correct format, the output is $\boxed{0.48}$

Editor

Python 3.13.1

0/0

Run code to see test results.

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