论文标题
凸层树
Convex Polytope Trees
论文作者
论文摘要
决策树通常仅限于使用单个超平面将其每个内部节点的协变空间分开。它通常需要大量的节点才能达到高精度，从而损害其解释性。在本文中，我们建议通过对其决策界限的可解释的概括来扩展决策树的家族。 CPT的每个节点的分裂函数基于一个加权概率不同的线性决策者的逻辑分离，该概率线性决策者也对应于协变量空间中的凸多角形。我们在每个节点上都使用非参数贝叶斯人来推断社区的规模，从而通过缩小多层方面的数量来鼓励更简单的决策界限。我们开发了一种贪婪的方法，用于在给出树结构时为树参数有效构建CPT和可扩展的端到端训练算法。我们从经验上证明了CPT对来自不同领域的几个现实世界分类和回归任务的现有最新决策树的效率。
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.
