Loss-Based Prior for CART and BART Models
针对贝叶斯加性回归树模型提出一种基于损失的新型先验，通过两个参数控制树的深度与分支平衡，并给出默认校准，在模拟和真实数据上验证效果。
We present a novel prior for tree topology within Bayesian Additive Regression Trees (BART) models. This approach quantifies the hypothetical loss in information and the loss due to complexity associated with choosing the “wrong” tree structure. The resulting prior distribution is compellingly geared toward sparsity — a critical feature considering BART models’ tendency to overfit. Our method incorporates prior knowledge into the distribution via two parameters that govern the tree’s depth and balance between its left and right branches. Additionally, we propose a default calibration for these parameters, offering an objective version of the prior. We demonstrate our method’s efficacy on both simulated and real datasets.