# GS-BART: Bayesian Additive Regression Trees with Graph-split Decision Rules

arXiv: https://arxiv.org/abs/2509.07166 · HTML: https://mlsanity.com/paper/2509.07166/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Sep 2025.

## Built on by (most cited first, 2 of 2)

- [Graph-Split Bayesian Causal Forest for Spatial Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2609.36046/) (2026)
- [Dynamic Spatial Bayesian Machine Learning Model: Applications to Intergenerational Economic Mobility and Geographic Income Inequality in the United States](https://mlsanity.com/paper/2610.00072/) (2026)

## Abstract (arXiv)

Ensemble decision tree methods such as XGBoost, Random Forest, and Bayesian Additive Regression Trees (BART) have gained enormous popularity in data science for their superior performance in machine learning regression and classification tasks. In this paper, we introduce a new Bayesian graph-split additive decision tree method, GS-BART, designed to enhance the performance of axis-parallel split-based BART for dependent data with graph structures. The proposed approach encodes input feature information into candidate graph sets and employs a flexible split rule that respects the graph topology when constructing decision trees. We consider a generalized nonparametric regression model using GS-BART and design a scalable informed MCMC algorithm to sample the decision trees of GS-BART. The algorithm leverages a gradient-based recursive algorithm on root directed spanning trees or chains. The superior performance of the method over conventional ensemble tree models and Gaussian process regression models is illustrated in various regression and classification tasks for spatial and network data analysis.