An adaptive trimming approach to Bayesian additive regression trees

Abstract

Abstract 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.

Keywords

• Robust regression
• Outliers
• Adaptive trimmed regression
• Bayesian additive regression trees
• Forecasting