In this work, we provide data stream algorithms that compute optimal splits in decision tree learning. In particular, given a data stream of observations $x_i$ and their labels $y_i$, the goal is to find the optimal split $j$ that divides the data into two sets such that the mean squared error (for regression) or misclassification rate and Gini impurity (for classification) is minimized. We provide several fast streaming algorithms that use sublinear space and a small number of passes for these problems. These algorithms can also be extended to the massively parallel computation model. Our work, while not directly comparable, complements the seminal work of Domingos-Hulten (KDD 2000) and Hulten-Spencer-Domingos (KDD 2001).

翻译：本文研究为决策树学习提供了计算最优分割点的数据流算法。具体而言，给定观测数据$x_i$及其标签$y_i$组成的数据流，目标在于找到最优分割点$j$，将数据划分为两个子集，使得均方误差（针对回归问题）或误分类率与基尼不纯度（针对分类问题）最小化。我们针对这些问题提出了多种快速流式算法，这些算法仅需亚线性存储空间和少量数据遍历次数。这些算法亦可扩展至大规模并行计算模型。尽管无法直接比较，本文工作对Domingos-Hulten（KDD 2000）与Hulten-Spencer-Domingos（KDD 2001）的开创性研究形成了重要补充。