  Bayesian Additive Regression Trees (BART) are a powerful semiparametric
ensemble learning technique for modeling nonlinear regression functions.
Although initially BART was proposed for predicting only continuous and binary
response variables, over the years multiple extensions have emerged that are
suitable for estimating a wider class of response variables (e.g. categorical
and count data) in a multitude of application areas. In this paper we describe
a Generalized framework for Bayesian trees and their additive ensembles where
the response variable comes from an exponential family distribution and hence
encompasses a majority of these variants of BART. We derive sufficient
conditions on the response distribution, under which the posterior concentrates
at a minimax rate, up to a logarithmic factor. In this regard our results
provide theoretical justification for the empirical success of BART and its
variants.
