Fully Nonparametric Bayesian Additive Regression Trees
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Bayesian Additive Regression Trees (BART) is fully Bayesian approach to modeling with ensembles of trees. BART can uncover complex regression functions with high dimensional regressors in a fairly automatic way and provide Bayesian quantification of the uncertainty through posterior. However, BART assumes IID normal errors. This strong parametric assumption can lead to misleading inference and predictive uncertainty. In this paper we use the classic Dirichlet process mixture (DPM) mechanism to nonparametrically model the error distribution. A key strength of BART is that default priors work reasonable well in a variety of problems. The challenge in extending BART is to choose hyperparameters of the DPM so that the strengths of standard BART approach is not lost when the errors are close to normal, but the DPM has the ability to adapt to non-normal errors.
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