Edward I. George, University of Pennsylvania

Multidimensional Monotonicity Discovery via mBART
Date
Apr 1, 2024, 12:25 pm1:25 pm

Details

Event Description

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 predictor effects, we introduce mBART, a constrained version of BART that incorporates monotonicity with a multivariate basis of monotone trees. When the relationship between y and x can be safely assumed to be monotone in a particular subset of the predictors, mBART can be used to constrain BART over those predictors to yield (i) function estimates that are smoother and more interpretable, (ii) better out-of-sample predictive performance and (iii) less post-data uncertainty. However, when such monotonicity assumptions are unavailable, mBART can still be deployed within a higher dimensional predictor space to estimate the Jordan decomposition of the underlying regression function into its monotone components. Deployed in this way and coupled with variable selection, mBART provides a new approach for the simultaneous discovery of both the increasing and decreasing effect regions of all the predictors. (This is joint work with H. Chipman, R. McCulloch and T. Shively).

Bio:  Ed George is the Universal Furniture Professor Emeritus of Statistics and Data Science, and former Chair of the Department of Statistics at the Wharton School of the University of Pennsylvania. He received his PhD from Stanford University, and has held previous faculty appointments at the University of Chicago and the University of Texas at Austin.
An elected Fellow of ASA, IMS and ISBA, he has served as Co-Editor of the Annals of Statistics, as Executive Editor of Statistical Science, as President of ISBA, as well as on the editorial boards of numerous journals. His research interests include Bayesian analysis, hierarchical modeling, model uncertainty, multiple shrinkage, predictive
inference, tree modeling, statistical decision theory and variable selection.

Event Category
S. S. Wilks Memorial Seminar in Statistics