# Accounting for shared covariates in semi-parametric Bayesian additive regression trees

arXiv: https://arxiv.org/abs/2108.07636 · HTML: https://mlsanity.com/paper/2108.07636/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 78 references that are in the map.
- First posted on arXiv 17 Aug 2021.

## Builds on (most cited first, 10 of 10)

- [ranger: A Fast Implementation of Random Forests for High Dimensional Data in C++ and R](https://mlsanity.com/paper/1508.04409/) (2015)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [On Theory for BART](https://mlsanity.com/paper/1810.00787/) (2018)
- [Bayesian Additive Regression Trees with Model Trees](https://mlsanity.com/paper/2006.07493/) (2020)
- [Semiparametric Mixed-Scale Models Using Shared Bayesian Forests](https://mlsanity.com/paper/1809.08521/) (2018)
- [VCBART: Bayesian trees for varying coefficients](https://mlsanity.com/paper/2003.06416/) (2020)
- [Bayesian Additive Regression Trees using Bayesian Model Averaging](https://mlsanity.com/paper/1507.00181/) (2015)
- [Nonparametric competing risks analysis using Bayesian Additive Regression Trees (BART)](https://mlsanity.com/paper/1806.11237/) (2018)

## Built on by (most cited first, 2 of 2)

- [Bayesian CART models for insurance claims frequency](https://mlsanity.com/paper/2303.01923/) (2023)
- [Semi-Parametric Bayesian Additive Regression Trees for Risk Prediction with High-Dimensional Epigenetic Signatures and Low-Dimensional Covariates](https://mlsanity.com/paper/2605.20143/) (2026)

## Abstract (arXiv)

We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for non-specified interactions and non-linearities. Previous semi-parametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid poor coverage properties and reduce bias in the estimates of the parameters in the linear predictor. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias and resolve non-identifiability issues between the parametric and non-parametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Our novel method is developed with a view to analysing data from an international education assessment, where certain predictors of students' achievements in mathematics are of particular interpretational interest. Through additional simulation studies and another application to a well-known benchmark dataset, we also show competitive performance when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods. The implementation of the proposed method is available at urlhttps://github.com/ebprado/CSP-BART.