GBDT-MO: Gradient-Boosted Decision Trees for Multiple Outputs

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Gradient-boosted decision trees (GBDTs) are widely used in machine learning, and the output of current GBDT implementations is a single variable. When there are multiple outputs, GBDT constructs multiple trees corresponding to the output variables. The correlations between variables are ignored by such a strategy causing redundancy of the learned tree structures. In this article, we propose a general method to learn GBDT for multiple outputs, called GBDT-MO. Each leaf of GBDT-MO constructs predictions of all variables or a subset of automatically selected variables. This is achieved by considering the summation of objective gains over all output variables. Moreover, we extend histogram approximation into the multiple-output case to speed up training. Various experiments on synthetic and real data sets verify that GBDT-MO achieves outstanding performance in terms of accuracy, training speed, and inference speed.