Society of Actuaries (SOA) PA Practice Exam

Which of the following is true regarding Gini as an impurity measure?

1. Higher values indicate better splits

2. It measures how often elements would be misclassified

3. It is the only impurity measure used in decision trees

4. It is less sensitive to node changes compared to classification error

The correct answer is: It measures how often elements would be misclassified

The Gini index, often utilized in decision trees, serves as a metric to quantify impurity within a dataset. Specifically, it helps in assessing how often a randomly chosen element from the set would be incorrectly classified if it were labeled according to the distribution of labels in the subset. When the Gini impurity is calculated, a lower value indicates a more homogeneous subset, meaning there’s a higher likelihood that an element from this subset will be classified correctly. This means that a Gini impurity close to zero corresponds to a situation where nearly all elements belong to a single class, reflecting a better split. Conversely, higher Gini values suggest greater impurity, indicating that the split is less effective for creating subsets that are rich in homogeneity. Understanding the properties of the Gini index demonstrates its functioning as a means of evaluating classification accuracy rather than simply being a standalone feature of decision trees. Other measures exist, such as entropy and classification error, and Gini is one of several methods employed. Hence, B accurately represents the role of Gini in measuring impurity and the misclassification potential within a dataset.