论文标题
与贝叶斯决策树合奏的自适应条件分配估计
Adaptive Conditional Distribution Estimation with Bayesian Decision Tree Ensembles
论文作者
论文摘要
我们提出了使用贝叶斯添加剂树（BART）的贝叶斯非参数模型，用于条件分布估计。我们使用的生成模型基于基本模型的拒绝采样。典型的BART模型，我们的模型是灵活的，具有默认的先验规范，并且在计算上很方便。为了解决我们提出的响应在巴特模型中的杰出作用，我们进一步引入了目标平滑的方法，该方法可能对巴特模型具有独立的兴趣。我们从理论上研究了所提出的模型，并为后验分布提供了足够的条件，可以在高维度中的平滑度类别上适应最小值的最佳速率，其中许多预测因子无关紧要。为了适应我们的模型，我们提出了一种数据增强算法，该算法允许现有的BART采样器以最小的努力扩展。我们说明了我们在模拟数据上的方法的性能，并使用它使用医疗支出小组调查（MEP）的数据来研究教育和体重指数之间的关系。
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. Typical of BART models, our model is flexible, has a default prior specification, and is computationally convenient. To address the distinguished role of the response in the BART model we propose, we further introduce an approach to targeted smoothing which is possibly of independent interest for BART models. 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).
