Linear Aggregation in Tree-based Estimators
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Regression trees and their ensemble methods are popular methods for non-parametric regression --- combining strong predictive performance with interpretable estimators. In order to improve their utility for smooth response surfaces, we study regression trees and random forests with linear aggregation functions. We introduce a new algorithm which finds the best axis-aligned split to fit optimal linear aggregation functions on the corresponding nodes and implement this method in the provably fastest way. This algorithm enables us to create more interpretable trees and obtain better predictive performance on a wide range of data sets. We also provide a software package that implements our algorithm. Applying the algorithm to several real-world data sets, we showcase its favorable performance in an extensive simulation study in terms of EMSE and demonstrate the improved interpretability of resulting estimators on a large real-world data set.
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