# Prediction with Missing Data via Bayesian Additive Regression Trees

arXiv: https://arxiv.org/abs/1306.0618 · HTML: https://mlsanity.com/paper/1306.0618/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2013.

## Built on by (most cited first, 10 of 10)

- [Fairness without Imputation: A Decision Tree Approach for Fair Prediction with Missing Values](https://mlsanity.com/paper/2109.10431/) (2021)
- [Interpretable Generalized Additive Models for Datasets with Missing Values](https://mlsanity.com/paper/2412.02646/) (2024)
- [Local Gaussian process extrapolation for BART models with applications to causal inference](https://mlsanity.com/paper/2204.10963/) (2022)
- [Leveraging Predictive Equivalence in Decision Trees](https://mlsanity.com/paper/2506.14143/) (2025)
- [Imputation of missing values in multi-view data](https://mlsanity.com/paper/2210.14484/) (2022)
- [Variable selection with missing data in both covariates and outcomes: Imputation and machine learning](https://mlsanity.com/paper/2104.02769/) (2021)
- [Extraction of Visual Information to Predict Crowdfunding Success](https://mlsanity.com/paper/2203.14806/) (2022)
- [Polar Encoding: A Simple Baseline Approach for Classification with Missing Values](https://mlsanity.com/paper/2210.01905/) (2022)
- [Bayesian Causal Forests for Longitudinal Data: Assessing the Impact of Part-Time Work on Growth in High School Mathematics Achievement](https://mlsanity.com/paper/2407.11927/) (2024)
- [Prediction Models That Learn to Avoid Missing Values](https://mlsanity.com/paper/2505.03393/) (2025)

## Abstract (arXiv)

We present a method for incorporating missing data in non-parametric statistical learning without the need for imputation. We focus on a tree-based method, Bayesian Additive Regression Trees (BART), enhanced with "Missingness Incorporated in Attributes," an approach recently proposed incorporating missingness into decision trees (Twala, 2008). This procedure takes advantage of the partitioning mechanisms found in tree-based models. Simulations on generated models and real data indicate that our proposed method can forecast well on complicated missing-at-random and not-missing-at-random models as well as models where missingness itself influences the response. Our procedure has higher predictive performance and is more stable than competitors in many cases. We also illustrate BART's abilities to incorporate missingness into uncertainty intervals and to detect the influence of missingness on the model fit.