Convex Polytope Trees
Convex Polytope Trees
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发表时间：
2020-10
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通讯作者：
Mohammadreza Armandpour;Mingyuan Zhou
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作者：
Mohammadreza Armandpour;Mingyuan Zhou
决策树通常被限制为使用单个超平面在其每个内部节点处分割协变量空间。它往往需要大量的节点才能达到高精度，这损害了它的可解释性。在这篇文章中，我们提出了凸多面树(CPT)，通过对决策树的决策边界进行可解释的推广，来扩展决策树族。CPT的每个节点上的分裂函数基于不同权重的概率线性决策者群体的逻辑析取，该群体在几何上也对应于协变量空间中的一个凸多面体。我们在每个节点使用非参数贝叶斯先验来推断社区的大小，通过缩小多面体方面的数量来鼓励更简单的决策边界。我们提出了一种贪婪的方法来高效地构造CPT，并且在给定树结构的情况下针对树参数提出了可扩展的端到端训练算法。在不同领域的几个实际分类和回归任务中，我们实证地证明了CPT在现有最先进的决策树上的有效性。
A decision tree is commonly restricted to use a single hyperplane to split the covariate space at each of its internal nodes. It often requires a large number of nodes to achieve high accuracy, hurting its interpretability. In this paper, we propose convex polytope trees (CPT) to expand the family of decision trees by an interpretable generalization of their decision boundary. The splitting function at each node of CPT is based on the logical disjunction of a community of differently weighted probabilistic linear decision-makers, which also geometrically corresponds to a convex polytope in the covariate space. We use a nonparametric Bayesian prior at each node to infer the community's size, encouraging simpler decision boundaries by shrinking the number of polytope facets. We develop a greedy method to efficiently construct CPT and scalable end-to-end training algorithms for the tree parameters when the tree structure is given. We empirically demonstrate the efficiency of CPT over existing state-of-the-art decision trees in several real-world classification and regression tasks from diverse domains.