Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles
Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles
复制标题
DOI：
10.1080/01621459.2022.2037431
复制
发表时间：
2022-03-17
影响因子：
3.7
通讯作者：
Murray, Jared
中科院分区：
文献类型：
--
作者：
Li, Yinpu;Linero, Antonio R.;Murray, Jared
提出了一种基于贝叶斯加性回归树的条件分布估计的贝叶斯非参数模型。我们使用的生成模型是基于对基本模型的拒绝抽样。与其他BART模型一样，我们的模型很灵活，具有默认的优先规范，并且在计算上很方便。为了解决响应在我们的BART模型中的独特作用，我们引入了一种独立感兴趣的BART模型的目标平滑方法。我们从理论上研究了所提出的模型，并给出了后验分布在许多预测器不相关的高维情形下自适应地集中在最小极大最优率超光滑类附近的充分条件。为了适应我们的模型，我们提出了一种数据增强算法，允许以最小的工作量扩展现有的BART采样器。我们说明了我们的方法在模拟数据上的表现，并使用来自医疗支出小组调查(MEPS)的数据来研究教育和身体质量指数之间的关系。有关本文的详细信息，可在网上找到。
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.