Predictive Distribution Modeling Using Transformation Forests
提出一种基于变换函数的参数化分布族方法，通过变换树和变换森林自适应估计条件分布，用于预测区间和概率预测，适合需要完整分布信息的回归问题。
Regression models for supervised learning problems with a continuous response are commonly understood as models for the conditional mean of the response given predictors. This notion is simple and therefore appealing for interpretation and visualization. Information about the whole underlying conditional distribution is, however, not available from these models. A more general understanding of regression models as models for conditional distributions allows much broader inference, for example, the computation of prediction intervals or probabilistic predictions for exceeding certain thresholds. Several random forest-type algorithms aim at estimating conditional distributions, most prominently quantile regression forests. We propose a novel approach based on a parametric family of distributions characterized by their transformation function. A dedicated novel “transformation tree” algorithm able to detect distributional changes is developed. Based on these transformation trees, we introduce “transformation forests” as an adaptive local likelihood estimator of conditional distribution functions. The resulting predictive distributions are fully parametric yet very general and allow inference procedures, such as likelihood-based variable importances, to be applied in a straightforward way. Supplemental files for this article are available online.