# Oblique Bayesian additive regression trees

arXiv: https://arxiv.org/abs/2411.08849 · HTML: https://mlsanity.com/paper/2411.08849/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 48 references that are in the map.
- First posted on arXiv 13 Nov 2024.

## Builds on (most cited first, 18 of 18)

- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Automated versus do-it-yourself methods for causal inference: Lessons learned from a data analysis competition](https://mlsanity.com/paper/1707.02641/) (2017)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Random-projection ensemble classification](https://mlsanity.com/paper/1504.04595/) (2015)
- [Sparse Projection Oblique Randomer Forests](https://mlsanity.com/paper/1506.03410/) (2015)
- [Canonical Correlation Forests](https://mlsanity.com/paper/1507.05444/) (2015)
- [Convergence Rates of Oblique Regression Trees for Flexible Function Libraries](https://mlsanity.com/paper/2210.14429/) (2022)
- [Semiparametric Mixed-Scale Models Using Shared Bayesian Forests](https://mlsanity.com/paper/1809.08521/) (2018)
- [Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles](https://mlsanity.com/paper/2005.02490/) (2020)
- [GP-BART: a novel Bayesian additive regression trees approach using Gaussian processes](https://mlsanity.com/paper/2204.02112/) (2022)
- [Density Regression with Bayesian Additive Regression Trees](https://mlsanity.com/paper/2112.12259/) (2021)
- [Linear Aggregation in Tree-based Estimators](https://mlsanity.com/paper/1906.06463/) (2019)
- [Model Mixing Using Bayesian Additive Regression Trees](https://mlsanity.com/paper/2301.02296/) (2023)
- [Manifold Oblique Random Forests: Towards Closing the Gap on Convolutional Deep Networks](https://mlsanity.com/paper/1909.11799/) (2019)
- [flexBART: Flexible Bayesian regression trees with categorical predictors](https://mlsanity.com/paper/2211.04459/) (2022)
- [Heteroscedastic BART Using Multiplicative Regression Trees](https://mlsanity.com/paper/1709.07542/) (2017)
- [BART-based inference for Poisson processes](https://mlsanity.com/paper/2005.07927/) (2020)
- [Combining Climate Models using Bayesian Regression Trees and Random Paths](https://mlsanity.com/paper/2407.13169/) (2024)

## Abstract (arXiv)

Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique trees, whose decision rules are based on linear combinations of features, can sometimes yield better predictions than axis-aligned trees and exhibit excellent theoretical properties. We develop an oblique version of BART that leverages a data-adaptive decision rule prior that recursively partitions the feature space along random hyperplanes. Using several synthetic and real-world benchmark datasets, we systematically compared our oblique BART implementation to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.