Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning

2026-05-07

AI Summary

This work addresses a key limitation in debiased machine learning: conventional covariate balancing methods often yield biased estimates of the average treatment effect (ATE) under treatment effect heterogeneity, as they neglect treatment-specific errors. To overcome this, the authors propose a regressor balancing framework guided by Neyman orthogonal scores, implemented via Riesz regression on the full set of covariates \(X\). This approach subsumes standard covariate balancing as a special case—valid only when score-related errors depend solely on covariates—and unifies existing balancing strategies through a synthesis of double machine learning and functional space projection. Theoretical analysis delineates the precise conditions under which covariate balancing is valid and demonstrates that regressor balancing achieves superior robustness and performance in general settings.

Abstract

This position paper argues that, in debiased machine learning, balancing functions should be derived from the Neyman orthogonal score, not chosen only as functions of covariates. Covariate balancing is effective when the regression error entering the score can be represented by functions of covariates alone, and it is the natural finite-dimensional approximation for targets such as ATT counterfactual means. For ATE estimation under treatment effect heterogeneity, however, the score error generally contains treatment-specific components because the outcome regression is a function of the full regressor $X=(D,Z)$. In that case, balancing common functions of $Z$ can leave the treatment-specific component unbalanced. We therefore advocate regressor balancing, implemented by Riesz regression with basis functions of $X$, as the general balancing principle for DML. The position is not that covariate balancing is invalid, but that covariate balancing should be understood as the special case that is appropriate when the score-relevant regression error is a function of covariates alone.

Problem

• covariate balancing
• Neyman orthogonal score
• treatment effect heterogeneity
• Riesz regression
• debiased machine learning

Innovation

• Neyman orthogonal score
• covariate balancing
• Riesz regression
• debiased machine learning
• treatment effect heterogeneity