发表机构
Snow Stallion AI; University of Antwerp（Snow Stallion AI; 安特卫普大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
介绍用于多元响应的双块聚类树，它是含局部多元线性模型叶子的确定性决策树，用双块降维，计算高效且可解释。还引入基于协偏度的降维空间估计器，能恢复分段线性模式，可与黑箱技术媲美，模型各部分可检查解释。
AI 中文摘要
双块聚类树（\tbtree）被引入作为一种用于多元响应的高度可解释回归树。双块树是确定性决策树，其叶子为局部多元线性模型，在局部叶子模型和杂质中使用密集或稀疏双块降维。所得模型计算高效且高度可解释。本文除了提出决策树估计器本身，还引入了基于最大化协偏度的双块降维空间估计器，便于识别数据中的非正态聚类。树本身产生一组局部线性模型，易于恢复分段线性模式，模拟对此进行了说明。两个真实数据示例表明双块树也能对更复杂的非线性依赖进行建模，且能与随机森林等黑箱建模技术相媲美。在每个点，生成分裂的双块模型以及叶子中的模型都可被检查和解释。
英文摘要
The twoblock clustering tree (\tbtree) is introduced as a highly interpretable regression tree for multivariate responses. Twoblock trees are deterministic decision trees that have local multivariate linear models as their leaves and use dense or sparse twoblock dimension reduction as local leaf models and in the impurity. The resulting models are both computationally efficient and can be highly interpretable. The estimator's primary aim is an interpretable, regime-aligned piecewise-linear description of the data, with predictive competitiveness retained as a constraint through a split/leaf decoupling. Beyond proposing the decision tree estimator itself, this paper also introduces an estimator for the twoblock dimension reduced space based on maximizing coskewness, which facilitates identification of non-normal clusters in the data. The tree inherently produces a set of local linear models and is therefore apt to recover piecewise linear regimes, which is illustrated in a simulation. However, two real-world data examples illustrate that twoblock trees are also capable of modeling more complexly nonlinear dependencies and can perform on par with black-box modeling techniques, such as random forests. At each point, both the twoblock models that generate the splits, as well as the ones in the leaves, can be inspected and interpreted.
