Prediction with Missing Data via Bayesian Additive Regression Trees

This article addresses prediction problems where covariate information is missing during model construction and is also missing in future observations for which we are obligated to generate a forecast. Our aim is to innovate a nonparametric statistical learning extension which incorporates missingness into both the training and the forecasting phases. In the spirit of nonparametric learning, we wish to incorporate the missingness in both phases automatically, without the need for pre-specified modeling. We limit our focus to tree-based statistical learning, which has demonstrated strong predictive performance and has consequently received considerable attention in recent years. State-of-the-art algorithms include Random Forests (RF, Breiman, 2001b), stochastic gradient boosting (Friedman, 2002), and Bayesian Additive and Regression Trees (BART, Chipman et al., 2010), the algorithm of interest in this study.