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BART: Bayesian Additive Regression Trees
Robert McCullough


We develop a Bayesian "sum-of-trees" model where each tree is constrained by a prior to be a weak learner. Fitting and inference are accomplished via an iterative backfitting MCMC algorithm. This model is motivated by ensemble methods in general, and boosting algorithms in particular. Like boosting, each weak learner (i.e., each weak tree) contributes a small amount to the overall model, and the training of a weak learner is conditional on the estimates for the other weak learners. The differences from the boosting algorithm are just as striking as the similarities: BART is defined by a statistical model: a prior and a likelihood, while boosting is defined by an algorithm. MCMC is used both to fit the model and to qualify predictive inference. The BART modelling strategy can also be viewed in the context of Bayesian non-parametrics. The key idea is to use a model which is rich enough to respond to a variety of signal types, but constrained by the prior from overreacting to weak signals. The ensemble approach provides for a rich base model form which can expand as needed via the MCMC mechanism. The priors are formulated so as to be interpretable, relatively easy to specify, and provide results that are stable across a wide range of prior hyperparameter values. The MCMC algorithm, which exhibits fast burn-in and good mixing, can be readily used for model averaging and for uncertainty assessment.

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