A0298
Title: Scalable targeted smoothing in high-dimensions with BART
Authors: Sameer Deshpande - University of Wisconsin--Madison (United States) [presenting]
Abstract: Bayesian additive regression trees (BART) is an easy-to-use and highly effective nonparametric regression model that approximates unknown functions with a sum of binary regression trees (i.e., piecewise-constant step functions). Consequently, BART is fundamentally limited in its ability to estimate smooth functions. Initial attempts to overcome this limitation replaced the constant output in each leaf of a tree with a realization of a Gaussian process (GP). While these elaborations are conceptually elegant, most implementations thereof are computationally prohibitive, displaying a nearly-cubic per-iteration complexity. A version of BART is proposed, built with trees that output linear combinations of ridge functions; that is, the trees return linear combinations of compositions between affine transforms of the inputs and a (potentially non-linear) activation function. A new MCMC sampler is developed to update trees in linear time. The proposed model includes a random Fourier feature-inspired approximation to treed GPs as a special case. More generally, the proposed model can be viewed as an ensemble of local neural networks, which combines the representational flexibility of neural networks with the uncertainty quantification and computational tractability of BART.
