Before the development of PILOT (PIecewise Linear Organic Tree), linear model trees were slow to fit and susceptible to overfitting, notably with large datasets. The traditional regression trees faced challenges capturing linear relationships efficiently. Linear model trees also encountered problems with interpretability when integrating linear models in leaf nodes. The research points out the need for algorithms that link the interpretability of decision tree with the accurate modelling of linear relationships.
The new approach introduced by PILOT to linear model trees addresses the prevalent limitations. It combines decision trees with linear models in leaf nodes, allowing PILOT to capture linear relationships more efficiently than standard trees. The algorithm applies techniques such as model selection and L2 boosting to ensure speed and stability without pruning. This approach retains the low complexity seen in CART (Classification and Regression Trees), while showcasing improved performance across various datasets.
Researchers from The University of Antwerp and KU Leuven have been exploring decision tree methods like CART and C4.5, popular for their quick training and interpretability. They found classical regression trees struggle with continuous relationships, leading to the development of model trees, especially linear model trees, allowing non-constant fits in leaf nodes. Existing methods such as FRIED and M5 face limitations concerning overfitting and high computational costs.
The introduction of PILOT provides a learning algorithm for developing linear model trees, which enhances decision tree interpretability and performance. PILOT uses a standard regression model with centred responses and design matrix X. It aggregates predictions from root to leaves, with theoretical discussions on consistency and improved convergence rates noted.
An experiment was conducted to test PILOT’s performance against other methods on various datasets using Wilcoxon signed rank tests. Datasets were preprocessed and scaled to ensure fair comparisons. Evaluation criteria included accuracy, stability, interpretability, and computational efficiency. The goal was to prove PILOT’s consistency in additive model settings and its performance on datasets generated by linear models.
Results indicate PILOT’s exceptional performance regarding efficiency and interpretability across numerous fields. It outperforms other tree-based methods, excelling where CART typically dominates. PILOT’s robust capacity to capture linear relationships reduces overfitting compared to alternative methods. Its interpretability, regularisation, and stability enhance decision-making processes.
In conclusion, PILOT, a novel algorithm for constructing linear model trees, offers speed, regularisation, stability, and interpretability. It outperforms existing methods on various datasets while maintaining computational efficiency comparable to CART. PILOT’s strengths include enhanced interpretability through leaf node linear models and a robust performance in capturing linear structures. The algorithm’s potential as a base learner for ensemble methods further emphasizes its versatility, making it a valuable tool for researchers and practitioners seeking a balance between model performance and explainability.
