We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for non-specified interactions and non-linearities. Previous semi-parametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid bias and poor coverage properties. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with bias/confounding between the parametric and non-parametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Through synthetic and real-world examples, we demonstrate that the performance of our novel semi-parametric BART is competitive when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods. The implementation of the proposed method is available at https://github.com/ebprado/CSP-BART.
翻译:我们提议对以巴耶西亚累进回归树(BART)为基础的半参数模型进行一些扩展。在半参数BART范式中,反应变量被线性预测器和BART模型所近似,即线性组成部分负责估计主要影响,而BART账户则负责估计非特定互动和非线性。以前以巴耶斯回归树(BART)为基础的半参数模型假定线性预测器和BART模型中的共变体是相互排斥的,目的是避免偏差和覆盖性差。我们的方法中的主要新颖之处在于我们如何改变巴埃特的树种变化,处理参数性和非参数性组成部分之间的偏差/裂,即使它们具有共同的共性。这使我们能够模拟涉及主要利益共变的复杂相互作用,既在它们之间,也与巴埃特部分中的共变体。我们通过合成和真实世界的实例,证明我们新型的半参数BART的性能在与回归模型、半参数性BART的替代配方和以树基/C为基础的其他方法相比是竞争性的。