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A central aspect of online decision tree solutions is evaluating the incomingdata and enabling model growth. For such, trees much deal with different kindsof input features and partition them to learn from the data. Numerical featuresare no exception, and they pose additional challenges compared to other kindsof features, as there is no trivial strategy to choose the best point to make asplit decision. The problem is even more challenging in regression tasksbecause both the features and the target are continuous. Typical onlinesolutions evaluate and store all the points monitored between split attempts,which goes against the constraints posed in real-time applications. In thispaper, we introduce the Quantization Observer (QO), a simple yet effectivehashing-based algorithm to monitor and evaluate split point candidates innumerical features for online tree regressors. QO can be easily integrated intoincremental decision trees, such as Hoeffding Trees, and it has a monitoringcost 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) anda linear cost to evaluate split points. Our extensive experimental setuphighlights QO's effectiveness in providing accurate split point suggestionswhile spending much less memory and processing time than its competitors.

Using dynamical quantization to perform split attempts in online tree regressors