Orthogonal Random Forest for Causal Inference

TL;DR

The paper introduces the orthogonal random forest, a novel method combining Neyman-orthogonality with random forests to improve causal inference, especially in high-dimensional settings, with proven consistency and asymptotic normality.

Contribution

It develops the orthogonal random forest algorithm that achieves oracle-like error rates for causal effect estimation with high-dimensional nuisance parameters.

Findings

Achieves the same error rate as an oracle under mild assumptions.

Allows control for high-dimensional variables under standard sparsity.

Provides empirical validation on synthetic and real datasets.

Abstract

We propose the orthogonal random forest, an algorithm that combines Neyman-orthogonality to reduce sensitivity with respect to estimation error of nuisance parameters with generalized random forests (Athey et al., 2017)--a flexible non-parametric method for statistical estimation of conditional moment models using random forests. We provide a consistency rate and establish asymptotic normality for our estimator. We show that under mild assumptions on the consistency rate of the nuisance estimator, we can achieve the same error rate as an oracle with a priori knowledge of these nuisance parameters. We show that when the nuisance functions have a locally sparse parametrization, then a local $\ell_1$-penalized regression achieves the required rate. We apply our method to estimate heterogeneous treatment effects from observational data with discrete treatments or continuous treatments, and we show that, unlike prior work, our method provably allows to control for a high-dimensional set of variables under standard sparsity conditions. We also provide a comprehensive empirical evaluation of our algorithm on both synthetic and real data.