二元决策树的又一种表示：一个数学论证
Yet Another Representation of Binary Decision Trees: A Mathematical Demonstration
AI总结：
本文提出一种基于位向量矩阵的决策树数值表示，将逻辑与运算转为算术运算，实现遍历，并统一扩展多种决策树。
摘要：
决策树看起来像一个简单的有向无环计算图，其中只有叶节点指定输出值，非终端节点指定其测试或分裂条件。从数值的角度，我们用计算图的语言来表达决策树。我们基于非终端节点的位向量，显式地参数化决策树的测试阶段、遍历阶段和预测阶段。如所示，决策树在某种意义上是一个浅层二元网络。特别地，我们引入位向量矩阵以数值方法实现树的遍历，其核心是将逻辑“与”运算转换为算术运算。我们将这种数值表示应用于概念上扩展和统一各种决策树。
英文摘要：
A decision tree looks like a simple directed acyclic computational graph, where only the leaf nodes specify the output values and the non-terminals specify their tests or split conditions. From the numerical perspective, we express decision trees in the language of computational graph. We explicitly parameterize the test phase, traversal phase and prediction phase of decision trees based on the bitvectors of non-terminal nodes. As shown, the decision tree is a shallow binary network in some sense. Especially, we introduce the bitvector matrix to implement the tree traversal in numerical approach, where the core is to convert the logical `AND' operation to arithmetic operations. And we apply this numerical representation to extend and unify diverse decision trees in concept.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
