# Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation

arXiv: https://arxiv.org/abs/2102.06573 · HTML: https://mlsanity.com/paper/2102.06573/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 60 references that are in the map.
- First posted on arXiv 12 Feb 2021.

## Builds on (most cited first, 19 of 19)

- [Estimation and Inference of Heterogeneous Treatment Effects using Random Forests](https://mlsanity.com/paper/1510.04342/) (2015)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Learning Representations for Counterfactual Inference](https://mlsanity.com/paper/1605.03661/) (2016)
- [Recursive Partitioning for Heterogeneous Causal Effects](https://mlsanity.com/paper/1504.01132/) (2015)
- [Bayesian Inference of Individualized Treatment Effects using Multi-task Gaussian Processes](https://mlsanity.com/paper/1704.02801/) (2017)
- [Theoretical Impediments to Machine Learning With Seven Sparks from the Causal Revolution](https://mlsanity.com/paper/1801.04016/) (2018)
- [Using simulation studies to evaluate statistical methods](https://mlsanity.com/paper/1712.03198/) (2017)
- [Some methods for heterogeneous treatment effect estimation in high-dimensions](https://mlsanity.com/paper/1707.00102/) (2017)
- [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)
- [A comparison of methods for model selection when estimating individual treatment effects](https://mlsanity.com/paper/1804.05146/) (2018)
- [Estimating Individual Treatment Effect in Observational Data Using Random Forest Methods](https://mlsanity.com/paper/1701.05306/) (2017)
- [Estimating Individual Treatment Effects using Non-Parametric Regression Models: a Review](https://mlsanity.com/paper/2009.06472/) (2020)
- [On Theory for BART](https://mlsanity.com/paper/1810.00787/) (2018)
- [Regularization and confounding in linear regression for treatment effect estimation](https://mlsanity.com/paper/1602.02176/) (2016)
- [Selective inference for effect modification via the lasso](https://mlsanity.com/paper/1705.08020/) (2017)
- [Statistical Causality from a Decision-Theoretic Perspective](https://mlsanity.com/paper/1405.2292/) (2014)
- [Better together? Statistical learning in models made of modules](https://mlsanity.com/paper/1708.08719/) (2017)
- [Semi-supervised learning and the question of true versus estimated propensity scores](https://mlsanity.com/paper/2009.06183/) (2020)

## Built on by (most cited first, 7 of 7)

- [Comparison of meta-learners for estimating multi-valued treatment heterogeneous effects](https://mlsanity.com/paper/2205.14714/) (2022)
- [Interpretable Deep Causal Learning for Moderation Effects](https://mlsanity.com/paper/2206.10261/) (2022)
- [Counterfactual Learning with Multioutput Deep Kernels](https://mlsanity.com/paper/2211.11119/) (2022)
- [Bayesian Causal Forests for Multivariate Outcomes: Application to Irish Data From an International Large Scale Education Assessment](https://mlsanity.com/paper/2303.04874/) (2023)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Bayesian X-Learner: Calibrated Posterior Inference for Heterogeneous Treatment Effects under Heavy-Tailed Outcomes](https://mlsanity.com/paper/2604.27394/) (2026)
- [Bayesian Mediation Analysis for Individualized Treatment Rules](https://mlsanity.com/paper/2607.28804/) (2026)

## Abstract (arXiv)

This paper develops a sparsity-inducing version of Bayesian Causal Forests, a recently proposed nonparametric causal regression model that employs Bayesian Additive Regression Trees and is specifically designed to estimate heterogeneous treatment effects using observational data. The sparsity-inducing component we introduce is motivated by empirical studies where not all the available covariates are relevant, leading to different degrees of sparsity underlying the surfaces of interest in the estimation of individual treatment effects. The extended version presented in this work, which we name Shrinkage Bayesian Causal Forest, is equipped with an additional pair of priors allowing the model to adjust the weight of each covariate through the corresponding number of splits in the tree ensemble. These priors improve the model's adaptability to sparse data generating processes and allow to perform fully Bayesian feature shrinkage in a framework for treatment effects estimation, and thus to uncover the moderating factors driving heterogeneity. In addition, the method allows prior knowledge about the relevant confounding covariates and the relative magnitude of their impact on the outcome to be incorporated in the model. We illustrate the performance of our method in simulated studies, in comparison to Bayesian Causal Forest and other state-of-the-art models, to demonstrate how it scales up with an increasing number of covariates and how it handles strongly confounded scenarios. Finally, we also provide an example of application using real-world data.