# Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles

arXiv: https://arxiv.org/abs/2005.02490 · HTML: https://mlsanity.com/paper/2005.02490/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2020.

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

- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)
- [Beyond Tides and Time: Machine Learning Triumph in Water Quality](https://mlsanity.com/paper/2309.16951/) (2023)
- [Room Occupancy Prediction: Exploring the Power of Machine Learning and Temporal Insights](https://mlsanity.com/paper/2312.14426/) (2023)
- [Oblique Bayesian additive regression trees](https://mlsanity.com/paper/2411.08849/) (2024)
- [Functional BART with Shape Priors: A Bayesian Tree Approach to Constrained Functional Regression](https://mlsanity.com/paper/2502.16888/) (2025)
- [Generative Regression with IQ-BART](https://mlsanity.com/paper/2507.04168/) (2025)

## Abstract (arXiv)

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Typical of BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in the BART model we propose, we further introduce an approach to targeted smoothing which is possibly of independent interest for BART models. We study the proposed model theoretically and provide sufficient conditions for the posterior distribution to concentrate at close to the minimax optimal rate adaptively over smoothness classes in the high-dimensional regime in which many predictors are irrelevant. To fit our model we propose a data augmentation algorithm which allows for existing BART samplers to be extended with minimal effort. We illustrate the performance of our methodology on simulated data and use it to study the relationship between education and body mass index using data from the medical expenditure panel survey (MEPS).