Bayesian Additive Regression Trees with Model Trees

TL;DR

This paper introduces MOTR-BART, an extension of BART that uses piecewise linear functions at nodes, improving efficiency and performance in capturing local linearities in regression and classification tasks.

Contribution

The paper proposes MOTR-BART, a novel extension of BART that employs linear predictors at nodes, reducing the number of trees needed for accurate predictions.

Findings

MOTR-BART achieves comparable or better performance than BART.

Fewer trees are required in MOTR-BART to reach similar accuracy.

Simulation and real data studies validate the effectiveness of MOTR-BART.

Abstract

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of non-linearity and high-order interactions. In this paper, we introduce an extension of BART, called Model Trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a linear predictor is estimated considering the covariates that have been used as the split variables in the corresponding tree. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART. Via simulation studies and real data applications, we compare MOTR-BART to its main competitors. R code for MOTR-BART implementation is available at https://github.com/ebprado/MOTR-BART.