Adversarial Estimation of Riesz Representers

TL;DR

This paper introduces an adversarial approach to estimate Riesz representers, enabling robust inference of linear functionals in causal models using various machine learning methods.

Contribution

It develops a novel adversarial estimation framework for Riesz representers applicable to multiple function spaces, with theoretical guarantees and practical inference methods.

Findings

Achieves near-optimal mean square rates based on the critical radius.

Compatible with targeted and debiased machine learning techniques.

Provides reliable inference in complex, nonlinear simulation settings.

Abstract

Many causal parameters are linear functionals of an underlying regression. The Riesz representer is a key component in the asymptotic variance of a semiparametrically estimated linear functional. We propose an adversarial framework to estimate the Riesz representer using general function spaces. We prove a nonasymptotic mean square rate in terms of an abstract quantity called the critical radius, then specialize it for neural networks, random forests, and reproducing kernel Hilbert spaces as leading cases. Our estimators are highly compatible with targeted and debiased machine learning with sample splitting; our guarantees directly verify general conditions for inference that allow mis-specification. We also use our guarantees to prove inference without sample splitting, based on stability or complexity. Our estimators achieve nominal coverage in highly nonlinear simulations where some previous methods break down. They shed new light on the heterogeneous effects of matching grants.