A0597
Title: Shape-constrained nonparametric high-dimensional function estimation using Bayesian additive regression trees
Authors: Hugh Chipman - Acadia University (Canada)
Edward George - University of Pennsylvania (United States)
Robert McCulloch - University of Chicago (United States)
Tom Shively - University of Texas at Austin (United States) [presenting]
Abstract: Bayesian additive regression tree (BART) models are a flexible method for nonparametrically estimating a high-dimensional function. We show how to extend BART models to incorporate shape constraints such as monotonicity. Such constraints arise naturally in many disciplines. For example, economic theory states that demand for a product is a monotonically decreasing function of its own price and a monotonically increasing function of its competitors prices. The imposition of shape constraints often results in much better function estimates than unconstrained methods provide. The stochastic search method we use to find promising BART models is different from the one used for unconstrained models because it is no longer possible to integrate out the function values at each node in a constrained model. In particular, decisions to split or collapse terminal nodes are made by conditioning on the function values at all other nodes. Also, new terminal node function values are generated individually or in pairs subject to the shape constraint. We show via simulation that for a wide range of high-dimensional functions the resulting constrained function estimates have good properties and are often a considerable improvement over unconstrained estimates.
