Prediction with Missing Data via Bayesian Additive Regression Trees

TL;DR

This paper introduces a Bayesian tree-based method that effectively handles missing data without imputation, improving prediction accuracy and stability in complex scenarios involving missingness.

Contribution

It extends Bayesian Additive Regression Trees with a novel approach to incorporate missingness directly into the model, enhancing predictive performance and interpretability.

Findings

Outperforms competitors in predictive accuracy and stability.

Effectively models missing-at-random and not-missing-at-random data.

Enables uncertainty quantification considering missingness.

Abstract

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.