  Random forests are an ensemble method relevant for many problems, such as
regression or classification. They are popular due to their good predictive
performance (compared to, e.g., decision trees) requiring only minimal tuning
of hyperparameters. They are built via aggregation of multiple regression trees
during training and are usually calculated recursively using hard splitting
rules. Recently regression forests have been incorporated into the framework of
distributional regression, a nowadays popular regression approach aiming at
estimating complete conditional distributions rather than relating the mean of
an output variable to input features only - as done classically. This article
proposes a new type of a distributional regression tree using a multivariate
soft split rule. One great advantage of the soft split is that smooth
high-dimensional functions can be estimated with only one tree while the
complexity of the function is controlled adaptive by information criteria.
Moreover, the search for the optimal split variable is obsolete. We show by
means of extensive simulation studies that the algorithm has excellent
properties and outperforms various benchmark methods, especially in the
presence of complex non-linear feature interactions. Finally, we illustrate the
usefulness of our approach with an example on probabilistic forecasts for the
Sun's activity.
