Recursive partitioning

Statistical method for decision tree construction

Recursive partitioning is a statistical method used for constructing decision trees. It is a fundamental technique in machine learning and data mining for classification and regression tasks. The method involves splitting a dataset into subsets, which are then split into further subsets, recursively, to form a tree structure. This process continues until the subsets are sufficiently homogeneous or meet other stopping criteria.

Overview

Recursive partitioning is used to create a model that predicts the value of a target variable based on several input variables. The process begins with the entire dataset and involves the following steps:

1. Splitting: The dataset is split into two or more homogeneous sets based on a splitting criterion. 2. Stopping: The process stops when a stopping criterion is met, such as a minimum number of samples in a node or a maximum tree depth. 3. Pruning: After the tree is fully grown, it may be pruned to remove branches that have little importance, which helps to prevent overfitting.

Splitting Criteria

The choice of splitting criterion is crucial for the performance of the decision tree. Common criteria include:

• Gini impurity: Measures the impurity of a node, used in classification and regression tree (CART) algorithms.
• Information gain: Used in ID3 and C4.5 algorithms, it measures the reduction in entropy.
• Variance reduction: Used for regression trees, it measures the reduction in variance of the target variable.

Applications

Recursive partitioning is widely used in various fields, including:

• Medicine: For diagnostic and prognostic models.
• Finance: For credit scoring and risk assessment.
• Marketing: For customer segmentation and targeting.

Advantages and Disadvantages

Advantages

• Interpretability: Decision trees are easy to interpret and visualize.
• Non-parametric: They do not assume any underlying distribution of the data.
• Versatility: Can handle both numerical and categorical data.

Disadvantages

• Overfitting: Trees can become overly complex and fit the noise in the data.
• Instability: Small changes in the data can result in a completely different tree.

Example

Decision tree for Titanic survivors

The image shows a decision tree constructed using recursive partitioning to predict the survival of passengers on the RMS Titanic. The tree splits the data based on features such as age, sex, and class, illustrating how recursive partitioning can be used to model complex relationships in data.

Related pages

• Decision tree learning
• Random forest
• Boosting (machine learning)
• Classification and regression tree