A Decision Tree is a flowchart-like structure used for classification and regression. Each internal node represents a test on a feature, each branch represents the outcome of the test, and each leaf node represents a final decision or classification.

🏗️ Building a Decision Tree

• Start with the full dataset.
• At each node, choose the best feature to split on.
• Repeat the process recursively for each child node until:
  • All data is classified perfectly, or
  • A stopping criterion is met (e.g., max depth, minimum samples, etc.).

🎯 Getting to the "Best" Decision Tree

• Goal: Find the tree that best classifies the data.
• Challenge: Finding the optimal decision tree is computationally infeasible.
  • It’s an NP-hard problem.
  • The number of possible trees grows exponentially with the number of features and data points.
  • At each node, we’d need to try all possible features and all possible ways to split them.

⚙️ A Practical Approach: Greedy Algorithms

Since finding the best tree is impractical, we use a greedy heuristic:

• At each step:
  • Evaluate all available features.
  • Choose the one that gives the best immediate improvement in performance (e.g., accuracy, information gain, Gini impurity).
  • Split on that feature and repeat recursively.

❓How Do We Choose the Best Feature?

• For each candidate feature:
  • Calculate the accuracy (or other metric) resulting from splitting the data on that feature.
  • Choose the feature that results in the highest accuracy (or other measure).
• Common criteria:
  • Accuracy (simple but not always robust)
  • Information Gain (used in ID3)
  • Gini Impurity (used in CART)
  • Gain Ratio, Chi-square, etc.