Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles

• 成果类型: Article
• 署名作者: Li, Yinpu; Linero, Antonio R.; Murray, Jared
• 署名单位: State University System of Florida; Florida State University; University of Texas System; University of Texas Austin
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2022.2037431
• 发表日期: 2023
• 页码: 2129-2142
• 关键词: logistic gaussian process; Nonparametric Regression; posterior consistency; quantile regression; models; mixtures; rates; bart

摘要

We present a Bayesian nonparametric model for conditional distribution estimation using Bayesian additive regression trees (BART). The generative model we use is based on rejection sampling from a base model. Like other BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in our BART model, we introduce an approach to targeted smoothing of BART models which is of independent interest. We study the proposed model theoretically and provide sufficient conditions for the posterior distribution to concentrate at close to the minimax optimal rate adaptively over smoothness classes in the high-dimensional regime in which many predictors are irrelevant. To fit our model, we propose a data augmentation algorithm which allows for existing BART samplers to be extended with minimal effort. We illustrate the performance of our methodology on simulated data and use it to study the relationship between education and body mass index using data from the medical expenditure panel survey (MEPS). for this article are available online.