# Co-data Learning for Bayesian Additive Regression Trees

arXiv: https://arxiv.org/abs/2311.09997 · HTML: https://mlsanity.com/paper/2311.09997/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 16 Nov 2023.

## Builds on (most cited first, 13 of 13)

- [Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC](https://mlsanity.com/paper/1507.04544/) (2015)
- [bartMachine: Machine Learning with Bayesian Additive Regression Trees](https://mlsanity.com/paper/1312.2171/) (2013)
- [Better prediction by use of co-data: Adaptive group-regularized ridge regression](https://mlsanity.com/paper/1411.3496/) (2014)
- [Variable selection for BART: An application to gene regulation](https://mlsanity.com/paper/1310.4887/) (2013)
- [Bayesian Additive Regression Trees using Bayesian Model Averaging](https://mlsanity.com/paper/1507.00181/) (2015)
- [Hierarchical Sparse Modeling: A Choice of Two Group Lasso Formulations](https://mlsanity.com/paper/1512.01631/) (2015)
- [Feature-weighted elastic net: using "features of features" for better prediction](https://mlsanity.com/paper/2006.01395/) (2020)
- [Adaptive penalization in high-dimensional regression and classification with external covariates using variational Bayes](https://mlsanity.com/paper/1811.02962/) (2018)
- [Flexible co-data learning for high-dimensional prediction](https://mlsanity.com/paper/2005.04010/) (2020)
- [Fast marginal likelihood estimation of penalties for group-adaptive elastic net](https://mlsanity.com/paper/2101.03875/) (2021)
- [ecpc: An R-package for generic co-data models for high-dimensional prediction](https://mlsanity.com/paper/2205.07640/) (2022)
- [Borrowing from Supplemental Sources to Estimate Causal Effects from a Primary Data Source](https://mlsanity.com/paper/2003.09680/) (2020)
- [Estimation of Predictive Performance in High-Dimensional Data Settings using Learning Curves](https://mlsanity.com/paper/2206.03825/) (2022)

## Abstract (arXiv)

Medical prediction applications often need to deal with small sample sizes compared to the number of covariates. Such data pose problems for prediction and variable selection, especially when the covariate-response relationship is complicated. To address these challenges, we propose to incorporate co-data, i.e. external information on the covariates, into Bayesian additive regression trees (BART), a sum-of-trees prediction model that utilizes priors on the tree parameters to prevent overfitting. To incorporate co-data, an empirical Bayes (EB) framework is developed that estimates, assisted by a co-data model, prior covariate weights in the BART model. The proposed method can handle multiple types of co-data simultaneously. Furthermore, the proposed EB framework enables the estimation of the other hyperparameters of BART as well, rendering an appealing alternative to cross-validation. We show that the method finds relevant covariates and that it improves prediction compared to default BART in simulations. If the covariate-response relationship is nonlinear, the method benefits from the flexibility of BART to outperform regression-based co-data learners. Finally, the use of co-data enhances prediction in an application to diffuse large B-cell lymphoma prognosis based on clinical covariates, gene mutations, DNA translocations, and DNA copy number data. Keywords: Bayesian additive regression trees; Empirical Bayes; Co-data; High-dimensional data; Omics; Prediction