title: Bayesian Ensemble Trees (BET) for Clustering and Prediction in Heterogeneous Data.
abstract: We propose a novel "tree-averaging" model that utilizes the ensemble of classification and regression trees (CART). Each constituent tree is estimated with a subset of similar data. We treat this grouping of subsets as Bayesian Ensemble Trees (BET) and model them as a Dirichlet process. We show that BET determines the optimal number of trees by adapting to the data heterogeneity. Compared with the other ensemble methods, BET requires much fewer trees and shows equivalent prediction accuracy using weighted averaging. Moreover, each tree in BET provides variable selection criterion and interpretation for each subset. We developed an efficient estimating procedure with improved estimation strategies in both CART and mixture models. We demonstrate these advantages of BET with simulations and illustrate the approach with a real-world data example involving regression of lung function measurements obtained from patients with cystic fibrosis. Supplemental materials are available online.
authors.affiliation: Department of Mathematical Sciences, University of Cincinnati.
authors.forename: Leo L
authors.initials: LL
authors.lastname: Duan
authors.affiliation: Division of Pulmonary Medicine, Cincinnati Children's Hospital Medical Center.
authors.forename: John P
authors.initials: JP
authors.lastname: Clancy
authors.affiliation: Division of Biostatistics and Epidemiology, Cincinnati Children's Hospital Medical Center.
authors.forename: Rhonda D
authors.initials: RD
authors.lastname: Szczesniak
keywords: Bayesian Mixture of Trees; Dirichlet Process; Ensemble Approach; Heterogeneity