Bayesian Decision Tree Ensembling Strategies for Nonparametric Problems

Abstract: In this talk we will make the case for using Bayesian decision tree ensembles, such as Bayesian additive regression trees (BART), for addressing some fully-nonparametric problems. We present models for density regression and survival analysis, and argue that our approaches are both easier to use and more effective than more standard Bayesian nonparametric solutions (such as those based on mixture models). On the applied side, we show how to use our models to extract interesting features across several datasets. On the theoretical side, we also show that our models attain minimax-optimal rates of convergence of the posterior in high-dimensional settings. Throughout the talk we will emphasize the flexibility and ease-of-use of our approach: we obtain excellent results on all simulated and real data analyses using heuristically chosen «default» priors, and our software tools make it quite straight-forward for researchers (both in-principle and in-practice) to embed our ensembles in larger models.