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Abstract:
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Bayesian additive regression trees (BART) is a flexible and scalable supervised learning model that offers accurate assessment of uncertainty via credible intervals. A strong assumption made by the BART model is that errors are iid. When error variance is nonconstant, point predictions from BART can still be accurate. However, credible intervals are unlikely to remain accurate or useful. Moreover, in many applied problems, understanding the relationship between the variance and predictors can be just as important as that of the mean model. We develop a novel heteroscedastic BART model to alleviate these concerns. Our approach is entirely non-parametric and does not rely on an a priori basis for the variance model. This is achieved through the introduction of Bayesian Multiplicative Trees, which model the variance component of BART as a function of the predictors. We implement the approach and demonstrate it in several examples.
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