CART Algorithm 🌲🏷️
CART (Classification and Regression Trees) is one of the most famous algorithms in data science. As the name suggests, it is a "Double Threat"—it can predict categories (Classification) AND numbers (Regression).
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1. Binary Splitting (The Great Divider)
Unlike CHAID, CART is a Binary Tree. This means every time it asks a question, it only allows two possible answers.
- The "Fork in the Road": Every node splits into exactly two child nodes (e.g., "Is Income > $50k?" -> Yes vs. No).
- Exhaustive Search: CART looks at every possible place it could "Cut" the data for every single variable and picks the one that splits the labels most clearly.
- Ease of Deployment: Because the logic is Always "Yes/No," CART models are incredibly easy to convert into simple "If-Then" rules for computer code.
- Handling All Data: It is "Data Neutral"—it can use both numbers (Age) and labels (Gender) effortlessly in the same tree.
2. Classification vs. Regression
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3. How it decides to split? (The Pursuit of Purity)
For classification, CART uses the Gini Index to measure "Impurity." For regression, it uses Variance Reduction.
- Gini Impurity (Chaos Measure): If a group has 50% "Buyers" and 50% "Non-Buyers," it is "Impure" (Gini = 0.5). CART wants to split this so that one group is 99% Buyers (Pure).
- Recursive Partitioning: The algorithm keeps splitting and re-splitting the groups until it either runs out of data or reaches a "Pure" result (Gini = 0).
- Feature Selection: It automatically identifies which variables are the most "Powerful" by placing them at the very top of the tree.
- Non-Parametric Nature: It doesn't care if your data follows a "Normal Distribution." It just looks at the raw numbers to find a split path.
4. Pruning: The Art of Trimming
A tree that is too big "Overfits," meaning it learns the specific names/dates of your old data instead of the general pattern. CART solves this using Pruning.
- Cost-Complexity Pruning: A mathematical trade-off where the algorithm "Cuts off" branches that add too much complexity without adding enough accuracy.
- The Healthy Tree: Pruning ensures that the final model is small enough for a human to understand but powerful enough to work on brand-new data.
- Validation Testing: The algorithm tests different versions of the "Trimmed" tree on a small slice of hidden data to find the "Perfect Size."
- Rule Simplification: It combines smaller, weak branches back into their parent nodes to reduce the "Noise" in the decision process.
Summary
- CART creates binary decision trees (2 branches only).
- It handles both Labels and Numbers.
- It uses Gini Impurity to find the best split.
- Pruning is used to keep the tree small and efficient.
Quiz Time! 🎯
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