Finding Decision Tree Splits in Streaming and Massively Parallel Models

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).