Robust Semiparametric Inference for Bayesian Additive Regression Trees
Abstract
We develop a semiparametric framework for inference on the mean response in missing-data settings using a corrected posterior distribution. Our approach is tailored to Bayesian Additive Regression Trees (BART), which is a powerful predictive method but whose nonsmoothness complicate asymptotic theory with multi-dimensional covariates. When using BART combined with Bayesian bootstrap weights, we establish a new Bernstein-von Mises theorem and show that the limit distribution generally contains a bias term. To address this, we introduce RoBART, a posterior bias-correction that robustifies BART for valid inference on the mean response. Monte Carlo studies support our theory, demonstrating reduced bias and improved coverage relative to existing procedures using BART.
Cite
@article{arxiv.2509.24634,
title = {Robust Semiparametric Inference for Bayesian Additive Regression Trees},
author = {Christoph Breunig and Ruixuan Liu and Zhengfei Yu},
journal= {arXiv preprint arXiv:2509.24634},
year = {2025}
}