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Abstract
We develop a Bayesian "sum-of-trees" model where each tree is constrained by a regularization
prior to be a weak learner, and fitting and inference are accomplished via an iterative
Bayesian backfitting MCMC algorithm that generates samples from a posterior. Effectively,
BART is a nonparametric Bayesian regression approach which uses dimensionally adaptive
random basis elements. Motivated by ensemble methods in general, and boosting algorithms
in particular, BART is defined by a statistical model: a prior and a likelihood. This
approach enables full posterior inference including point and interval estimates of
the unknown regression function as well as the marginal effects of potential predictors.
By keeping track of predictor inclusion frequencies, BART can also be used for model-free
variable selection. BART's many features are illustrated with a bake-off against competing
methods on 42 different data sets, with a simulation experiment and on a drug discovery
classification problem.
Comments Published in at http://dx.doi.org/10.1214/09-AOAS285 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org)