# Density Regression with Bayesian Additive Regression Trees

arXiv: https://arxiv.org/abs/2112.12259 · HTML: https://mlsanity.com/paper/2112.12259/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 22 Dec 2021.

## Built on by (most cited first, 6 of 6)

- [Generalized Bayesian Additive Regression Trees Models: Beyond Conditional Conjugacy](https://mlsanity.com/paper/2202.09924/) (2022)
- [Benchmarking Tabular Foundation Models for Conditional Density Estimation in Regression](https://mlsanity.com/paper/2603.26611/) (2026)
- [SoftBart: Soft Bayesian Additive Regression Trees](https://mlsanity.com/paper/2210.16375/) (2022)
- [A Bayesian Additive Regression Tree Model for Learning Conditional Average Treatment Effects in Regression Discontinuity Designs](https://mlsanity.com/paper/2503.00326/) (2025)
- [Oblique Bayesian additive regression trees](https://mlsanity.com/paper/2411.08849/) (2024)
- [Generative Regression with IQ-BART](https://mlsanity.com/paper/2507.04168/) (2025)

## Abstract (arXiv)

Flexibly modeling how an entire density changes with covariates is an important but challenging generalization of mean and quantile regression. While existing methods for density regression primarily consist of covariate-dependent discrete mixture models, we consider a continuous latent variable model in general covariate spaces, which we call DR-BART. The prior mapping the latent variable to the observed data is constructed via a novel application of Bayesian Additive Regression Trees (BART). We prove that the posterior induced by our model concentrates quickly around true generative functions that are sufficiently smooth. We also analyze the performance of DR-BART on a set of challenging simulated examples, where it outperforms various other methods for Bayesian density regression. Lastly, we apply DR-BART to two real datasets from educational testing and economics, to study student growth and predict returns to education. Our proposed sampler is efficient and allows one to take advantage of BART's flexibility in many applied settings where the entire distribution of the response is of primary interest. Furthermore, our scheme for splitting on latent variables within BART facilitates its future application to other classes of models that can be described via latent variables, such as those involving hierarchical or time series data.