  Random Forest (Breiman, 2001) is a successful and widely used regression and
classification algorithm. Part of its appeal and reason for its versatility is
its (implicit) construction of a kernel-type weighting function on training
data, which can also be used for targets other than the original mean
estimation. We propose a novel forest construction for multivariate responses
based on their joint conditional distribution, independent of the estimation
target and the data model. It uses a new splitting criterion based on the MMD
distributional metric, which is suitable for detecting heterogeneity in
multivariate distributions. The induced weights define an estimate of the full
conditional distribution, which in turn can be used for arbitrary and
potentially complicated targets of interest. The method is very versatile and
convenient to use, as we illustrate on a wide range of examples. The code is
available as Python and R packages drf.
