Era Splitting -- Invariant Learning for Decision Trees

Real-life machine learning problems exhibit distributional shifts in the data from one time to another or from one place to another. This behavior is beyond the scope of the traditional empirical risk minimization paradigm, which assumes i.i.d. distribution of data over time and across locations. The emerging field of out-of-distribution (OOD) generalization addresses this reality with new theory and algorithms which incorporate environmental, or era-wise information into the algorithms. So far, most research has been focused on linear models and/or neural networks. In this research we develop two new splitting criteria for decision trees, which allow us to apply ideas from OOD generalization research to decision tree models, namely, gradient boosting decision trees (GBDT). The new splitting criteria use era-wise information associated with the data to grow tree-based models that are optimal across all disjoint eras in the data, instead of optimal over the entire data set pooled together, which is the default setting. In this paper, two new splitting criteria are defined and analyzed theoretically. Effectiveness is tested on four experiments, ranging from simple, synthetic to complex, real-world applications. In particular we cast the OOD domain-adaptation problem in the context of financial markets, where the new models out-perform state-of-the-art GBDT models on the Numerai data set. The new criteria are incorporated into the Scikit-Learn code base and made freely available online.