To obtain a probabilistic model for a dependent variable based on some set of
explanatory variables, a distributional approach is often adopted where the
parameters of the distribution are linked to regressors. In many classical
models this only captures the location of the distribution but over the last
decade there has been increasing interest in distributional regression
approaches modeling all parameters including location, scale, and shape.
Notably, so-called non-homogeneous Gaussian regression (NGR) models both mean
and variance of a Gaussian response and is particularly popular in weather
forecasting. Moreover, generalized additive models for location, scale, and
shape (GAMLSS) provide a framework where each distribution parameter is modeled
separately capturing smooth linear or nonlinear effects. However, when variable
selection is required and/or there are non-smooth dependencies or interactions
(especially unknown or of high-order), it is challenging to establish a good
GAMLSS. A natural alternative in these situations would be the application of
regression trees or random forests but, so far, no general distributional
framework is available for these. Therefore, a framework for distributional
regression trees and forests is proposed that blends regression trees and
random forests with classical distributions from the GAMLSS framework as well
as their censored or truncated counterparts. To illustrate these novel
approaches in practice, they are employed to obtain probabilistic precipitation
forecasts at numerous sites in a mountainous region based on a large number of
numerical weather prediction quantities. It is shown that the novel
distributional regression forests automatically select variables and
interactions, performing on par or often even better than GAMLSS specified
either through prior meteorological knowledge or a computationally more
demanding boosting approach.

提出了一种将回归树与随机森林与经典 GAMLSS 框架中的分布并置合并的分布回归树和随机森林框架，以用于变量选择和建模非平滑依赖关系或高阶交互作用的情况，将其应用于大量气象预测数据生成的降水概率预测，并发现这种方法可以自动选择变量和交互作用，性能与计算成本高的提前预测信息或增强方法 GAMLSS 的性能相当甚至更好。