Current implementations of Bayesian Additive Regression Trees (BART) are based on axis-aligned decision rules that recursively partition the feature space using a single feature at a time. Several authors have demonstrated that oblique trees, whose decision rules are based on linear combinations of features, can sometimes yield better predictions than axis-aligned trees and exhibit excellent theoretical properties. We develop an oblique version of BART that leverages a data-adaptive decision rule prior that recursively partitions the feature space along random hyperplanes. Using several synthetic and real-world benchmark datasets, we systematically compared our oblique BART implementation to axis-aligned BART and other tree ensemble methods, finding that oblique BART was competitive with -- and sometimes much better than -- those methods.

翻译：当前贝叶斯加性回归树（BART）的实现基于轴对齐决策规则，这些规则每次使用单个特征递归划分特征空间。多位学者已证明，基于特征线性组合的斜向决策树有时能比轴对齐树产生更好的预测结果，并展现出优异的理论性质。我们开发了一种斜向版本的BART，其利用数据自适应的决策规则先验，通过随机超平面对特征空间进行递归划分。基于多个合成与真实世界基准数据集，我们系统性地将斜向BART实现与轴对齐BART及其他树集成方法进行比较，发现斜向BART与这些方法具有竞争力——有时甚至显著优于它们。