标题： 用贝叶斯回归树集成拟合稀疏高维变系数模型 显示英文标题

标题： Fitting sparse high-dimensional varying-coefficient models with Bayesian regression tree ensembles

摘要： 通过允许线性回归模型中$p$协变量的影响作为$R$额外效应修饰因子的函数而变化，变系数模型（VCMs）在经典统计中流行的可解释但刚性的参数模型和机器学习中流行的灵活但不透明的方法之间取得了引人注目的平衡。但在高维情况下，当$p$和/或$R$超过观测数时，现有的拟合VCM方法无法识别哪些协变量具有非零效应以及哪些效应修饰因子驱动这些效应。我们提出了sparseVCBART，这是一种完全贝叶斯模型，它用回归树集成近似VCM中的每个系数函数，并通过回归树叶输出的全局-局部收缩先验和每棵树分割概率的分层先验来鼓励稀疏性。我们证明了sparseVCBART后验以接近最小最大最优的速率收缩，自动适应真实系数函数的未知稀疏结构和平滑性。与现有最先进的方法相比，sparseVCBART实现了具有竞争力的预测准确性，并且不确定性区间明显更窄且校准更好，尤其是在零协变量效应的情况下。我们使用sparseVCBART来研究人际对话对偏见的影响如何根据受访者的政治和人口统计特征而变化。 显示英文摘要

摘要： By allowing the effects of $p$ covariates in a linear regression model to vary as functions of $R$ additional effect modifiers, varying-coefficient models (VCMs) strike a compelling balance between interpretable-but-rigid parametric models popular in classical statistics and flexible-but-opaque methods popular in machine learning. But in high-dimensional settings where $p$ and/or $R$ exceed the number of observations, existing approaches to fitting VCMs fail to identify which covariates have a non-zero effect and which effect modifiers drive these effects. We propose sparseVCBART, a fully Bayesian model that approximates each coefficient function in a VCM with a regression tree ensemble and encourages sparsity with a global--local shrinkage prior on the regression tree leaf outputs and a hierarchical prior on the splitting probabilities of each tree. We show that the sparseVCBART posterior contracts at a near-minimax optimal rate, automatically adapting to the unknown sparsity structure and smoothness of the true coefficient functions. Compared to existing state-of-the-art methods, sparseVCBART achieved competitive predictive accuracy and substantially narrower and better-calibrated uncertainty intervals, especially for null covariate effects. We use sparseVCBART to investigate how the effects of interpersonal conversations on prejudice could vary according to the political and demographic characteristics of the respondents.