  This paper develops a novel stochastic tree ensemble method for nonlinear
regression, which we refer to as XBART, short for Accelerated Bayesian Additive
Regression Trees. By combining regularization and stochastic search strategies
from Bayesian modeling with computationally efficient techniques from recursive
partitioning approaches, the new method attains state-of-the-art performance:
in many settings it is both faster and more accurate than the widely-used
XGBoost algorithm. Via careful simulation studies, we demonstrate that our new
approach provides accurate point-wise estimates of the mean function and does
so faster than popular alternatives, such as BART, XGBoost and neural networks
(using Keras). We also prove a number of basic theoretical results about the
new algorithm, including consistency of the single tree version of the model
and stationarity of the Markov chain produced by the ensemble version.
Furthermore, we demonstrate that initializing standard Bayesian additive
regression trees Markov chain Monte Carlo (MCMC) at XBART-fitted trees
considerably improves credible interval coverage and reduces total run-time.
