Orthogonal Random Forest for Causal Inference

We propose orthogonal random forest, an algorithm that incorporates double machine learning---a method of using Neyman-orthogonal moments to reduce sensitivity with respect to nuisance parameters to estimate the target parameter---with generalized random forests---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 assumption 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 data and real data, and show that it consistently outperforms baseline approaches.