# Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects

arXiv: https://arxiv.org/abs/1706.09523 · HTML: https://mlsanity.com/paper/1706.09523/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2017.

## Built on by (most cited first, 30 of 41)

- [Foundation Models for Causal Inference via Prior-Data Fitted Networks](https://mlsanity.com/paper/2506.10914/) (2025)
- [Robust and Agnostic Learning of Conditional Distributional Treatment Effects](https://mlsanity.com/paper/2205.11486/) (2022)
- [A Tree-based Model Averaging Approach for Personalized Treatment Effect Estimation from Heterogeneous Data Sources](https://mlsanity.com/paper/2103.06261/) (2021)
- [Safe Policy Learning through Extrapolation: Application to Pre-trial Risk Assessment](https://mlsanity.com/paper/2109.11679/) (2021)
- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Statistical Inference for Heterogeneous Treatment Effects Discovered by Generic Machine Learning in Randomized Experiments](https://mlsanity.com/paper/2203.14511/) (2022)
- [Feature Selection for Discovering Distributional Treatment Effect Modifiers](https://mlsanity.com/paper/2206.00516/) (2022)
- [Stochastic Tree Ensembles for Estimating Heterogeneous Effects](https://mlsanity.com/paper/2209.06998/) (2022)
- [Local Gaussian process extrapolation for BART models with applications to causal inference](https://mlsanity.com/paper/2204.10963/) (2022)
- [Meta-Learners for Estimation of Causal Effects: Finite Sample Cross-Fit Performance](https://mlsanity.com/paper/2201.12692/) (2022)
- [Double Robust Bayesian Inference on Average Treatment Effects](https://mlsanity.com/paper/2211.16298/) (2022)
- [Variable Importance Matching for Causal Inference](https://mlsanity.com/paper/2302.11715/) (2023)
- [Causal Q-Aggregation for CATE Model Selection](https://mlsanity.com/paper/2310.16945/) (2023)
- [The Connection Between R-Learning and Inverse-Variance Weighting for Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2307.09700/) (2023)
- [Generalization Bounds for Causal Regression: Insights, Guarantees and Sensitivity Analysis](https://mlsanity.com/paper/2405.09516/) (2024)
- [Improve ROI with Causal Learning and Conformal Prediction](https://mlsanity.com/paper/2407.01065/) (2024)
- [Causal Inference with the Instrumental Variable Approach and Bayesian Nonparametric Machine Learning](https://mlsanity.com/paper/2102.01199/) (2021)
- [Accounting for shared covariates in semi-parametric Bayesian additive regression trees](https://mlsanity.com/paper/2108.07636/) (2021)
- [Distributionally Robust Causal Inference with Observational Data](https://mlsanity.com/paper/2210.08326/) (2022)
- [Is merging worth it? Securely evaluating the information gain for causal dataset acquisition](https://mlsanity.com/paper/2409.07215/) (2024)
- [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)
- [Treatment response as a latent variable](https://mlsanity.com/paper/2502.08776/) (2025)
- [A Bayesian Additive Regression Tree Model for Learning Conditional Average Treatment Effects in Regression Discontinuity Designs](https://mlsanity.com/paper/2503.00326/) (2025)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [Improving RCT-Based Treatment Effect Estimation Under Covariate Mismatch via Calibrated Alignment](https://mlsanity.com/paper/2603.19186/) (2026)
- [Tailoring Strictly Proper Scoring Rules for Downstream Tasks: An Application to Causal Inference](https://mlsanity.com/paper/2606.03332/) (2026)
- [Dive into Decision Trees and Forests: A Theoretical Demonstration](https://mlsanity.com/paper/2101.08656/) (2021)
- [Deep Bayesian Estimation for Dynamic Treatment Regimes with a Long Follow-up Time](https://mlsanity.com/paper/2109.11929/) (2021)

## Abstract (arXiv)

This paper presents a novel nonlinear regression model for estimating heterogeneous treatment effects from observational data, geared specifically towards situations with small effect sizes, heterogeneous effects, and strong confounding. Standard nonlinear regression models, which may work quite well for prediction, have two notable weaknesses when used to estimate heterogeneous treatment effects. First, they can yield badly biased estimates of treatment effects when fit to data with strong confounding. The Bayesian causal forest model presented in this paper avoids this problem by directly incorporating an estimate of the propensity function in the specification of the response model, implicitly inducing a covariate-dependent prior on the regression function. Second, standard approaches to response surface modeling do not provide adequate control over the strength of regularization over effect heterogeneity. The Bayesian causal forest model permits treatment effect heterogeneity to be regularized separately from the prognostic effect of control variables, making it possible to informatively "shrink to homogeneity". We illustrate these benefits via the reanalysis of an observational study assessing the causal effects of smoking on medical expenditures as well as extensive simulation studies.