A machine learning technique merging Bayesian method called Bayesian Additive Regression Trees (BART) provides a nonparametric Bayesian approach that further needs improved forecasting accuracy in the presence of outliers, especially when dealing with potential nonlinear relationships and complex interactions among the response and explanatory variables, which poses a major challenge in forecasting. This study proposes an adaptive trimmed regression method using BART, dubbed BART(Atr) to improve forecasting accuracy by identifying suspected outliers effectively and removing these outliers in the analysis. Through extensive simulations across various scenarios, the effectiveness of BART(Atr) is evaluated against three alternative methods: default BART, robust linear modeling with Huber’s loss function, and data-driven robust regression with Huber’s loss function. The simulation results consistently show BART(Atr) outperforming the other three methods. To demonstrate its practical application, BART(Atr) is applied to the well-known Boston Housing Price dataset, a standard regression analysis example. Furthermore, random attack templates are introduced on the dataset to assess BART(Atr)’s performance under such conditions.

一种融合贝叶斯方法（称为贝叶斯加性回归树 (BART)）的机器学习技术提供了一种非参数贝叶斯方法，该方法进一步需要在存在异常值的情况下提高预测准确性，特别是在处理潜在的非线性关系以及响应和解释变量之间的复杂相互作用时，对预测提出了重大挑战。本研究提出了一种使用 BART 的自适应修剪回归方法，称为 BART(Atr)，通过有效识别可疑异常值并在分析中删除这些异常值来提高预测准确性。通过跨各种场景的广泛模拟，根据三种替代方法评估了 BART(Atr) 的有效性：默认 BART、使用 Huber 损失函数的稳健线性建模以及使用 Huber 损失函数的数据驱动稳健回归。仿真结果一致表明 BART(Atr) 优于其他三种方法。为了演示其实际应用，将 BART(Atr) 应用于著名的波士顿房价数据集，这是一个标准回归分析示例。此外，数据集上引入了随机攻击模板，以评估 BART(Atr) 在此类条件下的性能。