The Art of BART: Minimax Optimality over Nonhomogeneous Smoothness in High Dimension

Many asymptotically minimax procedures for function estimation often rely on somewhat arbitrary and restrictive assumptions such as isotropy or spatial homogeneity. This work enhances the theoretical understanding of Bayesian additive regression trees under substantially relaxed smoothness assumptions. We provide a comprehensive study of asymptotic optimality and posterior contraction of Bayesian forests when the regression function has anisotropic smoothness that possibly varies over the function domain. The regression function can also be possibly discontinuous. We introduce a new class of sparse …

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