Multidimensional Monotonicity Discovery with MBART

• Activity Number: 320 - Practical and Realistic Variable Selection Methods
• Type: Invited
• Date/Time: Tuesday, July 31, 2018 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Edward George* and Robert McCulloch and Hugh Chipman and Tom Shively
• Companies: Wharton, University of Pennsylvania and Arizona State University and Acadia University and University of Texas at Austin
• Keywords: BART; Bayesian nonparametrics; nonconjugate MCMC; shape constrained estimation; trees

Abstract

For the discovery of a regression relationship between y and x, a vector of p potential predictors, the flexible nonparametric nature of BART (Bayesian Additive Regression Trees) allows for a much richer set of possibilities than restrictive parametric approaches. To exploit the potential monotonicity of the predictors, we introduce mBART, a constrained version of BART that incorporates monotonicity with a multivariate basis of monotone trees, thereby avoiding the further confines of a full parametric form. Using mBART to estimate such effects yields (i) function estimates that are smoother and more interpretable, (ii) better out-of-sample predictive performance and (iii) less post-data uncertainty. By using mBART to simultaneously estimate both the increasing and the decreasing regions of a predictor, mBART opens up a new approach to the discovery and estimation of the decomposition of a function into its monotone components.