# On Theory for BART

arXiv: https://arxiv.org/abs/1810.00787 · HTML: https://mlsanity.com/paper/1810.00787/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Oct 2018.

## Built on by (most cited first, 17 of 17)

- [Shrinkage Bayesian Causal Forests for Heterogeneous Treatment Effects Estimation](https://mlsanity.com/paper/2102.06573/) (2021)
- [Bridging Breiman's Brook: From Algorithmic Modeling to Statistical Learning](https://mlsanity.com/paper/2102.12328/) (2021)
- [A Mixing Time Lower Bound for a Simplified Version of BART](https://mlsanity.com/paper/2210.09352/) (2022)
- [Sharded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2306.00361/) (2023)
- [On Mixing Rates for Bayesian CART](https://mlsanity.com/paper/2306.00126/) (2023)
- [Accounting for shared covariates in semi-parametric Bayesian additive regression trees](https://mlsanity.com/paper/2108.07636/) (2021)
- [Hierarchical Embedded Bayesian Additive Regression Trees](https://mlsanity.com/paper/2204.07207/) (2022)
- [Single MCMC Chain Parallelisation on Decision Trees](https://mlsanity.com/paper/2207.12688/) (2022)
- [Parallel Approaches to Accelerate Bayesian Decision Trees](https://mlsanity.com/paper/2301.09090/) (2023)
- [Ranking Perspective for Tree-based Methods with Applications to Symbolic Feature Selection](https://mlsanity.com/paper/2410.02623/) (2024)
- [Horseshoe Forests for High-Dimensional Causal Survival Analysis](https://mlsanity.com/paper/2507.22004/) (2025)
- [BFTS: Thompson Sampling with Bayesian Additive Regression Trees](https://mlsanity.com/paper/2602.07767/) (2026)
- [Adaptive Bayesian Sum of Trees Model for Covariate Dependent Spectral Analysis](https://mlsanity.com/paper/2109.14677/) (2021)
- [Generalized Bayesian Additive Regression Trees: Theory and Software](https://mlsanity.com/paper/2304.12505/) (2023)
- [Bayesian Decision Trees Inspired from Evolutionary Algorithms](https://mlsanity.com/paper/2305.18774/) (2023)
- [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)

Ensemble learning is a statistical paradigm built on the premise that many weak learners can perform exceptionally well when deployed collectively. The BART method of Chipman et al. (2010) is a prominent example of Bayesian ensemble learning, where each learner is a tree. Due to its impressive performance, BART has received a lot of attention from practitioners. Despite its wide popularity, however, theoretical studies of BART have begun emerging only very recently. Laying the foundations for the theoretical analysis of Bayesian forests, Rockova and van der Pas (2017) showed optimal posterior concentration under conditionally uniform tree priors. These priors deviate from the actual priors implemented in BART. Here, we study the exact BART prior and propose a simple modification so that it also enjoys optimality properties. To this end, we dive into branching process theory. We obtain tail bounds for the distribution of total progeny under heterogeneous Galton-Watson (GW) processes exploiting their connection to random walks. We conclude with a result stating the optimal rate of posterior convergence for BART.