# Local Gaussian process extrapolation for BART models with applications to causal inference

arXiv: https://arxiv.org/abs/2204.10963 · HTML: https://mlsanity.com/paper/2204.10963/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 34 references that are in the map.
- First posted on arXiv 23 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Predictive inference with the jackknife+](https://mlsanity.com/paper/1905.02928/) (2019)
- [Balancing Covariates via Propensity Score Weighting](https://mlsanity.com/paper/1609.07494/) (2016)
- [Bayesian regression tree models for causal inference: regularization, confounding, and heterogeneous effects](https://mlsanity.com/paper/1706.09523/) (2017)
- [Stochastic tree ensembles for regularized nonlinear regression](https://mlsanity.com/paper/2002.03375/) (2020)
- [Prediction with Missing Data via Bayesian Additive Regression Trees](https://mlsanity.com/paper/1306.0618/) (2013)
- [Addressing Positivity Violations in Causal Effect Estimation using Gaussian Process Priors](https://mlsanity.com/paper/2110.10266/) (2021)

## Built on by (most cited first, 5 of 5)

- [Stochastic Tree Ensembles for Estimating Heterogeneous Effects](https://mlsanity.com/paper/2209.06998/) (2022)
- [Extrapolation-Aware Nonparametric Statistical Inference](https://mlsanity.com/paper/2402.09758/) (2024)
- [BARK: A Fully Bayesian Tree Kernel for Black-box Optimization](https://mlsanity.com/paper/2503.05574/) (2025)
- [LOCUS: A Distribution-Free Loss-Quantile Score for Risk-Aware Predictions](https://mlsanity.com/paper/2603.01971/) (2026)
- [CREDO: Epistemic-Aware Conformalized Credal Envelopes for Regression](https://mlsanity.com/paper/2603.06826/) (2026)

## Abstract (arXiv)

Bayesian additive regression trees (BART) is a semi-parametric regression model offering state-of-the-art performance on out-of-sample prediction. Despite this success, standard implementations of BART typically provide inaccurate prediction and overly narrow prediction intervals at points outside the range of the training data. This paper proposes a novel extrapolation strategy that grafts Gaussian processes to the leaf nodes in BART for predicting points outside the range of the observed data. The new method is compared to standard BART implementations and recent frequentist resampling-based methods for predictive inference. We apply the new approach to a challenging problem from causal inference, wherein for some regions of predictor space, only treated or untreated units are observed (but not both). In simulation studies, the new approach boasts superior performance compared to popular alternatives, such as Jackknife+.