Wasserstein Random Forests and Applications in Heterogeneous Treatment Effects

TL;DR

This paper introduces Wasserstein-based variants of Random Forests for improved estimation of conditional distributions in causal inference, especially for heterogeneous treatment effects, supported by theoretical insights and numerical experiments.

Contribution

It proposes Wasserstein distance-based modifications to Random Forests for better conditional distribution estimation in causal inference, extending the algorithm to multivariate outputs.

Findings

Enhanced estimation of conditional distributions in complex causal scenarios.

Theoretical connections between Wasserstein distances and Random Forests.

Numerical experiments demonstrate improved interpretability and accuracy.

Abstract

We present new insights into causal inference in the context of Heterogeneous Treatment Effects by proposing natural variants of Random Forests to estimate the key conditional distributions. To achieve this, we recast Breiman's original splitting criterion in terms of Wasserstein distances between empirical measures. This reformulation indicates that Random Forests are well adapted to estimate conditional distributions and provides a natural extension of the algorithm to multivariate outputs. Following the philosophy of Breiman's construction, we propose some variants of the splitting rule that are well-suited to the conditional distribution estimation problem. Some preliminary theoretical connections are established along with various numerical experiments, which show how our approach may help to conduct more transparent causal inference in complex situations.