Notes
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CART

CART is one of the most common ways to build a decision tree that can make predictions by asking a sequence of simple questions about the input features. If you’ve seen a flowchart like “if income > 50k then … else …”, you already have the basic idea.

What CART is and how it builds a tree

CART stands for Classification and Regression Trees. It’s a single framework that produces:

  • a classification tree (predicts a category, like “spam” vs “not spam”), or
  • a regression tree (predicts a number, like house price).

CART grows a tree by repeatedly choosing a binary split (two-way split) of the data at each node. For numeric features it tests thresholds (e.g., “age ≤ 37.5”), and for categorical features it tests membership in a set of categories. The goal is to make the child nodes “purer” than the parent.

What objective it optimizes

For classification, CART typically chooses splits that reduce Gini impurity (or sometimes cross-entropy). For regression, it chooses splits that reduce mean squared error, which is equivalent to reducing variance within each leaf. Predictions at the leaves are simple: a majority class for classification, or the mean target value for regression.

Why it matters in real projects

CART trees are fast, handle mixed feature types, and are easy to explain—useful for credit scoring, churn prediction, and fraud triage. The catch is that an unpruned tree can overfit badly, memorizing noise. CART addresses this with cost-complexity pruning (trading accuracy for simplicity). In scikit-learn, this is the idea behind `DecisionTreeClassifier` / `DecisionTreeRegressor` settings like `max_depth`, `min_samples_leaf`, and `ccp_alpha`.

CART (Classification and Regression Trees) is a decision-tree algorithm that learns a binary tree by recursively splitting features to predict either a discrete class label or a continuous value. It typically selects splits by minimizing impurity (e.g., Gini) for classification or squared error for regression, producing piecewise-constant predictions at leaves. CART matters because it is a strong, interpretable baseline and the standard tree learner underlying ensembles like random forests and gradient-boosted trees.

Think of a game of “20 Questions,” where each question narrows down the answer: “Is it bigger than a breadbox?” “Is it an animal?” That’s the basic feel of CART, which stands for Classification and Regression Trees.

CART is a way for an AI system to make decisions by asking a sequence of simple yes/no-style questions about the information it’s given. It can do two jobs: classification (pick a category, like “spam” vs “not spam”) and regression (predict a number, like a house price). The result is a tree-like set of rules that’s often easy to understand and explain.