# Hierarchical Embedded Bayesian Additive Regression Trees

arXiv: https://arxiv.org/abs/2204.07207 · HTML: https://mlsanity.com/paper/2204.07207/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 44 references that are in the map.
- First posted on arXiv 14 Apr 2022.

## Builds on (most cited first, 11 of 11)

- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [On Theory for BART](https://mlsanity.com/paper/1810.00787/) (2018)
- [Penalising model component complexity: A principled, practical approach to constructing priors](https://mlsanity.com/paper/1403.4630/) (2014)
- [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)
- [Bayesian quantile additive regression trees](https://mlsanity.com/paper/1607.02676/) (2016)
- [Log-Linear Bayesian Additive Regression Trees for Multinomial Logistic and Count Regression Models](https://mlsanity.com/paper/1701.01503/) (2017)
- [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 Causal Forests for Longitudinal Data: Assessing the Impact of Part-Time Work on Growth in High School Mathematics Achievement](https://mlsanity.com/paper/2407.11927/) (2024)
- [Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States](https://mlsanity.com/paper/2610.00072/) (2026)

## Abstract (arXiv)

We propose a simple yet powerful extension of Bayesian Additive Regression Trees which we name Hierarchical Embedded BART (HE-BART). The model allows for random effects to be included at the terminal node level of a set of regression trees, making HE-BART a non-parametric alternative to mixed effects models which avoids the need for the user to specify the structure of the random effects in the model, whilst maintaining the prediction and uncertainty calibration properties of standard BART. Using simulated and real-world examples, we demonstrate that this new extension yields superior predictions for many of the standard mixed effects models' example data sets, and yet still provides consistent estimates of the random effect variances. In a future version of this paper, we outline its use in larger, more advanced data sets and structures.