Thought I had this cold and then halfway through my answer I realized I was conflating information gain with Gini impurity without being clear about when you'd use one over the other.
Start by defining what a split is and why it's needed, then explain the mechanics of evaluating candidate splits using impurity measures, and finally discuss practical considerations like greedy algorithms and overfitting. Use a concrete example to illustrate the process.
Pro tip: Mention that decision trees use greedy, recursive partitioning, and that the choice of splitting criterion (e.g., Gini vs. entropy) often has little practical impact, but handling continuous features and missing values requires careful engineering.
Explain that splitting aims to partition data into subsets that are as homogeneous as possible with respect to the target variable, reducing impurity.
Introduce common impurity metrics like Gini impurity, entropy (information gain), and variance reduction for regression, and how they quantify the quality of a split.
Outline the greedy search over features and thresholds (for continuous features) to find the split that maximizes impurity decrease, and mention that this is done recursively.
Mention that splitting continues until a stopping condition (e.g., max depth, min samples) is met, and that pruning can combat overfitting.
Talk about computational complexity, handling categorical vs. continuous features, missing values, and the trade-offs between different splitting criteria.
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