Decision Tree in Regression

By Fawad Ahmad

Details: BSc. Data Science

Published: June 16, 2024 17:45

A decision tree in regression, also known as a regression tree, is a type of decision tree designed to predict continuous values rather than categorical outcomes.

1. Splitting the Data: The process begins with the entire dataset. The algorithm searches through all possible splits of all features to find the split that minimizes a certain criterion, such as the mean squared error (MSE) or mean absolute error (MAE). The goal is to find the split that results in the most homogeneous subgroups (i.e., the groups where the target values are as similar as possible). 2. Calculating Impurity: For regression trees, impurity is typically measured using variance, MSE, or MAE. The variance reduction (or reduction in MSE/MAE) is calculated for each possible split, and the split that provides the greatest reduction in impurity is chosen. 3. Creating Nodes and Leaves: Once the best split is identified, the data is divided into two subsets. This process is recursively applied to each subset, creating nodes in the tree, until a stopping criterion is met. This criterion can be a minimum number of samples per leaf, a maximum tree depth, or an impurity threshold. 4. Predicting Values: When a new data point needs to be predicted, it is passed down the tree, following the decision rules at each node, until it reaches a leaf. The prediction for that data point is the average value of the target variable for the training samples in that leaf. Example: Assume we are predicting house prices based on features like size, location, and number of rooms. The decision tree will: Start with the entire dataset and search for the feature and split point that minimize the MSE of house prices. Split the data into two groups based on the chosen feature and split point. Repeat this process recursively for each group, continuing to split the data into more homogeneous subgroups. Stop splitting when further splits do not significantly reduce the MSE or another stopping criterion is met. Advantages and Disadvantages: Advantages: Interpretability: Regression trees are easy to visualize and interpret. Non-linearity: They can model non-linear relationships without requiring feature transformation. Feature Importance: They can inherently indicate the most important features in predicting the target variable. Disadvantages: Overfitting: They can easily overfit, especially if the tree is very deep. Instability: Small changes in the data can result in a completely different tree. Bias-Variance Tradeoff: They may have high variance and low bias, requiring techniques like pruning or ensemble methods (e.g., Random Forests) to improve performance. Pruning: To combat overfitting, pruning methods are used. This involves removing parts of the tree that do not provide significant power in predicting the target variable, based on a validation set or by setting complexity parameters. Conclusion: Regression trees are a powerful and intuitive tool for predictive modeling of continuous variables. By understanding how to construct and refine these trees, practitioners can leverage them effectively for a wide range of applications.