Using dynamical quantization to perform split attempts in online tree regressors

Abstract: A central aspect of online decision tree solutions is evaluating the incoming data and enabling model growth. For such, trees much deal with different kinds of input features and partition them to learn from the data. Numerical features are no exception, and they pose additional challenges compared to other kinds of features, as there is no trivial strategy to choose the best point to make a split decision. The problem is even more challenging in regression tasks because both the features and the target are continuous. Typical online solutions evaluate and store all the points monitored between split attempts, which goes against the constraints posed in real-time applications. In this paper, we introduce the Quantization Observer (QO), a simple yet effective hashing-based algorithm to monitor and evaluate split point candidates in numerical features for online tree regressors. QO can be easily integrated into incremental decision trees, such as Hoeffding Trees, and it has a monitoring cost of $O(1)$ per instance and sub-linear cost to evaluate split candidates. Previous solutions had a $O(\log n)$ cost per insertion (in the best case) and a linear cost to evaluate split points. Our extensive experimental setup highlights QO's effectiveness in providing accurate split point suggestions while spending much less memory and processing time than its competitors.