Regresipuiden

Regresipuiden, often translated as regression trees, are a type of decision tree used in machine learning for regression tasks. Unlike classification trees that predict categorical outcomes, regression trees predict continuous numerical values. The fundamental principle involves recursively partitioning the feature space into smaller, more homogeneous regions. At each node of the tree, a split is made based on a feature and a threshold value, aiming to minimize the variance or mean squared error of the target variable within the resulting child nodes.

The process starts with the entire dataset at the root node. The algorithm iteratively searches for the best split that reduces the impurity, typically measured by the sum of squared errors. Once a split is determined, the data is divided into two subsets, and the process is repeated for each subset at new child nodes. This recursive partitioning continues until a stopping criterion is met, such as a maximum tree depth, a minimum number of samples in a leaf node, or when no further split can significantly reduce the impurity.

When making a prediction for a new data point, it traverses the tree from the root down to a terminal leaf node. The predicted value for that data point is typically the average of the target values of the training samples that ended up in that same leaf node. Regression trees are interpretable models, allowing for a visual understanding of how predictions are made based on feature values. However, they can be prone to overfitting, and techniques like pruning or ensemble methods such as Random Forests and Gradient Boosting are often employed to improve their generalization performance.