Distributional Random Forests: Heterogeneity Adjustment and Multivariate Distributional Regression

TL;DR

This paper introduces Distributional Random Forests, a novel method for modeling multivariate response distributions using a new splitting criterion based on the MMD metric, enabling flexible heterogeneity adjustment and distributional regression.

Contribution

It proposes a new forest construction for multivariate responses using MMD-based splitting, allowing estimation of full conditional distributions independent of specific targets.

Findings

Effective heterogeneity detection in multivariate distributions

Versatile distributional regression applicable to various examples

Available implementation in Python and R packages

Abstract

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.