Decision Trees: How They Work and When to Use Them

Decision trees are among the most intuitive and visually interpretable algorithms in machine learning. They mimic the way humans make decisions: by asking a series of questions, each narrowing down the possibilities until a conclusion is reached. If you have ever played the game Twenty Questions, you already understand the basic principle behind decision trees. This natural decision-making process, encoded as an algorithm, turns out to be a remarkably powerful tool for both classification and regression.

How Decision Trees Work

A decision tree is a tree-shaped structure where each internal node represents a test on a feature (e.g., "Is the temperature above 30 degrees?"), each branch represents an outcome of that test, and each leaf node represents a prediction (a class label for classification or a value for regression).

The algorithm builds the tree by recursively splitting the data into subsets based on the feature and threshold that best separate the target classes (or best reduce the variance for regression). This process is called recursive partitioning.

To make a prediction for a new data point, you start at the root node and follow the branches based on the data point's feature values until you reach a leaf node. The prediction at that leaf is your answer.

Splitting Criteria: How the Tree Decides

The critical question in building a decision tree is: at each node, which feature and threshold should we split on? The answer depends on the splitting criterion, which measures how well a split separates the classes.

For Classification

• Gini Impurity: Measures the probability that a randomly chosen element would be incorrectly classified. A Gini of 0 means the node is pure (all elements belong to one class). The algorithm chooses splits that minimize Gini impurity.
• Information Gain (Entropy): Based on information theory, entropy measures the disorder or uncertainty in a dataset. Information gain is the reduction in entropy after a split. The algorithm chooses splits that maximize information gain.

For Regression

• Mean Squared Error (MSE): The algorithm splits on the feature and threshold that minimizes the total MSE in the resulting child nodes. Each leaf predicts the mean of the target values in that subset.
• Mean Absolute Error (MAE): Similar to MSE but uses absolute errors, making it more robust to outliers.

"A decision tree is the closest thing machine learning has to a human-readable explanation. You can literally follow the logic from root to leaf and understand exactly why the model made its prediction." - This interpretability is the tree's greatest strength.

The Overfitting Problem

Left unchecked, a decision tree will keep splitting until every leaf contains a single data point, perfectly memorizing the training data. This is called overfitting, and it means the model captures noise rather than genuine patterns, leading to poor performance on new data.

Several techniques combat overfitting in decision trees:

1. Maximum depth: Limit how deep the tree can grow. Shallower trees are simpler and generalize better.
2. Minimum samples per leaf: Require each leaf to contain at least a minimum number of samples, preventing the tree from creating overly specific rules.
3. Minimum samples for split: Require a minimum number of samples at a node before allowing a split.
4. Pruning: Build the full tree first, then remove branches that do not improve performance on a validation set. This post-processing step simplifies the tree without losing predictive power.

Advantages and Disadvantages

Advantages

• Interpretability: Decision trees are among the most interpretable ML models. They can be visualized and explained to non-technical stakeholders.
• No feature scaling needed: Unlike logistic regression and SVMs, decision trees are not sensitive to the scale of input features.
• Handle mixed data types: Trees can work with both numerical and categorical features without preprocessing.
• Capture nonlinear relationships: Trees can model complex nonlinear boundaries that linear models cannot.
• Feature importance: Trees naturally provide a ranking of feature importance based on how much each feature contributes to reducing impurity.

Disadvantages

• Overfitting: Without careful pruning or constraints, trees easily memorize training data.
• Instability: Small changes in the data can produce drastically different tree structures.
• Biased toward dominant classes: In imbalanced datasets, trees tend to favor the majority class.
• Axis-aligned splits: Standard trees only split parallel to feature axes, making them inefficient at capturing diagonal decision boundaries.

When to Use Decision Trees

Decision trees shine when interpretability is paramount, when you need to explain your model to business stakeholders, regulators, or patients. They are excellent for exploratory data analysis and feature selection. They serve as the foundation for ensemble methods that are among the most powerful ML algorithms available.

In practice, you will rarely deploy a single decision tree in production. Instead, you will use Random Forests or gradient boosting algorithms like XGBoost, LightGBM, or CatBoost, which combine hundreds or thousands of trees to achieve superior accuracy while mitigating individual tree weaknesses.

"Decision trees are like democracy: one tree might make a bad decision, but a forest of trees voting together usually gets it right. This is the fundamental insight behind Random Forests." - A metaphor for ensemble learning.

Decision trees remain one of the most important algorithms in machine learning, not because they are the most accurate individual predictor, but because they are the most intuitive, interpretable, and versatile building block in the ML toolkit. Master decision trees, and you have the key to understanding an entire family of powerful algorithms.