用自适应软分叉规则提升决策树对复杂边界的建模能力
SBAMDT: Bayesian Additive Decision Trees with Adaptive Soft Semi-multivariate Split Rules
- 采用概率软分叉机制，融合单变量与多变量特征进行灵活分割
- 动态适应不同节点的平滑度需求，在合成数据和纽约教育数据上表现更优
- 适合需要精确不确定性量化和复杂非线性关系建模的场景
贝叶斯加法回归树（BART）因出色的预测性能和不确定性量化能力而广受欢迎。然而，传统决策树在每个节点仅依赖单一变量的确定性分割，难以有效捕捉复杂决策边界，尤其在空间域或多变量交互场景下表现受限。本文提出一种新型概率加法决策树模型——SBAMDT，采用软分叉规则，可同时利用单变量与多变量特征进行灵活分割，并保留特征空间的几何特性。该概率分叉规则在不同决策节点间自适应调整，能有效应对回归函数变化平滑度的差异。实验表明，该模型在合成数据集和纽约市教育数据集上的表现优于现有树模型。
原文摘要 · Abstract (English)
Bayesian Additive Regression Trees [BART, Chipman et al., 2010] have gained significant popularity due to their remarkable predictive performance and ability to quantify uncertainty. However, standard decision tree models rely on recursive data splits at each decision node, using deterministic decision rules based on a single univariate feature. This approach limits their ability to effectively capture complex decision boundaries, particularly in scenarios involving multiple features, such as spatial domains, or when transitions are either sharp or smoothly varying. In this paper, we introduce a novel probabilistic additive decision tree model that employs a soft split rule. This method enables highly flexible splits that leverage both univariate and multivariate features, while also respecting the geometric properties of the feature domain. Notably, the probabilistic split rule adapts dynamically across decision nodes, allowing the model to account for varying levels of smoothness in the regression function. We demonstrate the utility of the proposed model through comparisons with existing tree-based models on synthetic datasets and a New York City education dataset.
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