Gini Impurity

Decision-tree classifiers recursively divide data into regions. At each candidate split, the tree needs a criterion for how well the resulting child nodes separate class labels. Gini impurity for a node is 1 minus the sum of squared class proportions. For classes with proportions p_k, G = 1 - sum(p_k squared). A pure node has one proportion equal to one and all others zero, so G is zero. In a binary node with balanced proportions 0.5 and 0.5, G is 0.5, the maximum for two classes. For a hypothetical node with 8 positive and 2 negative cases, proportions are 0.8 and 0.2. The calculation is 1 - (0.64 + 0.04) = 0.32. This score can be interpreted as the probability of misclassification if a label is assigned by randomly drawing according to the node's class proportions, though a trained tree normally predicts the majority class. CART evaluates candidate splits by the weighted average impurity in the children, weighting each by its share of the parent observations. The impurity decrease is parent impurity minus this weighted child impurity. Thus an empty-looking or very small child does not automatically make a split useful. Tree constraints such as minimum leaf size, depth and pruning also affect the final model. Gini is computationally convenient because it avoids logarithms, while entropy uses -sum(p log p) and may rank candidate splits similarly but not necessarily identically. Gini impurity is not the same as the dataset's overall class imbalance, a probability that the model's prediction is wrong, or an evaluation score on held-out data. It is calculated locally at a node from labels present there. A tree can achieve pure training leaves by growing deeply and still generalize poorly. Evaluate the full model with an appropriate split, and inspect class-specific errors, calibration where needed and stability. The impurity criterion guides construction; it does not establish whether features are causal or predictions useful.