# Bayesian Additive Regression Trees with Model Trees

arXiv: https://arxiv.org/abs/2006.07493 · HTML: https://mlsanity.com/paper/2006.07493/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2020.

## Built on by (most cited first, 11 of 11)

- [GP-BART: a novel Bayesian additive regression trees approach using Gaussian processes](https://mlsanity.com/paper/2204.02112/) (2022)
- [Accounting for shared covariates in semi-parametric Bayesian additive regression trees](https://mlsanity.com/paper/2108.07636/) (2021)
- [Hierarchical Embedded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2204.07207/) (2022)
- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)
- [Bayesian CART models for insurance claims frequency](https://mlsanity.com/paper/2303.01923/) (2023)
- [From predictions to confidence intervals: an empirical study of conformal prediction methods for in-context learning](https://mlsanity.com/paper/2504.15722/) (2025)
- [Bayesian Causal Forests for Multivariate Outcomes: Application to Irish Data From an International Large Scale Education Assessment](https://mlsanity.com/paper/2303.04874/) (2023)
- [Bayesian Additive Regression Networks](https://mlsanity.com/paper/2404.04425/) (2024)
- [BARMPy: Bayesian Additive Regression Models Python Package](https://mlsanity.com/paper/2404.04738/) (2024)
- [Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regression](https://mlsanity.com/paper/2502.16888/) (2025)
- [SplitWise Regression: Stepwise Modeling with Adaptive Dummy Encoding](https://mlsanity.com/paper/2505.15423/) (2025)

## Abstract (arXiv)

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.