# An Infinite BART model

arXiv: https://arxiv.org/abs/2511.20087 · HTML: https://mlsanity.com/paper/2511.20087/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 4 of its 23 references that are in the map.
- First posted on arXiv 25 Nov 2025.

## Builds on (most cited first, 4 of 4)

- [Discussion on "Bayesian Regression Tree Models for Causal Inference: Regularization, Confounding, and Heterogeneous Effects" by Hahn, Murray and Carvalho](https://mlsanity.com/paper/2108.02836/) (2021)
- [Bayesian Regression Tree Ensembles that Adapt to Smoothness and Sparsity](https://mlsanity.com/paper/1707.09461/) (2017)
- [Fully Nonparametric Bayesian Additive Regression Trees](https://mlsanity.com/paper/1807.00068/) (2018)
- [Non-parametric Bayesian inference via loss functions under model misspecification](https://mlsanity.com/paper/2103.04086/) (2021)

## Abstract (arXiv)

Bayesian additive regression trees (BART) is a popular Bayesian ensemble model used in regression and classification analysis. Under this modeling framework, the regression function is approximated by an ensemble of decision trees, interpreted as weak learners. In this work, we propose a generalization of the BART model that has two main features: first, it automatically selects the number of decision trees using the given data; second, the model allows clusters of observations to have different regression functions since each data point can only use a selection of weak learners, instead of all of them. This model generalization is accomplished by including a binary weight matrix in the conditional distribution of the response variable, which activates only a specific subset of decision trees for each observation. Such a matrix is endowed with an Indian Buffet process prior, and sampled within the MCMC sampler, together with the other BART parameters. We then compare the Infinite BART model with the classic one on simulated and real datasets. Specifically, we provide examples illustrating variable importance, partial dependence and causal estimation.