  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 paper, 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 multiple output case to speed up the training process.
Various experiments on synthetic and real-world datasets verify that GBDT-MO
achieves outstanding performance in terms of both accuracy and training speed.
Our codes are available on-line.
