Bayesian and Empirical Bayesian Forests

We derive ensembles of decision trees through a nonparametric Bayesian model, allowing us to view such ensembles as samples from a posterior distribution. This insight motivates a class of Bayesian Forest (BF) algorithms that provide small gains in performance and large gains in interpretability. Based on the BF framework, we are able to show that high-level tree hierarchy is stable in large samples. This motivates an empirical Bayesian Forest (EBF) algorithm for building approximate BFs on massive distributed datasets and we show that EBFs outperform sub-sampling based alternatives by a large margin.