Kato Advocates Riesz Regression Guided by Neyman Score

According to the arXiv submission arXiv:2605.06386 (submitted 7 May 2026), Masahiro Kato presents a position paper arguing that balancing functions in debiased machine learning should be derived from the Neyman orthogonal score rather than selected only as functions of covariates. The paper frames covariate balancing as valid when the regression error entering the orthogonal score is representable by covariate-only functions, and it cites ATT targets as a setting where covariate balancing is a natural finite-dimensional approximation (arXiv:2605.06386). The paper further states that for ATE estimation under treatment-effect heterogeneity the score error generally includes treatment-specific components because the outcome regression depends on the full regressor, and that balancing shared covariate functions can leave those components unbalanced (arXiv:2605.06386).

Per the paper, the recommended remedy is regressor balancing, operationalized through Riesz regression using basis functions of the full regressor. The author positions Riesz regression as a way to approximate the regression error relevant to the orthogonal score (arXiv:2605.06386). The paper emphasizes that this is not a rejection of covariate balancing; rather, covariate balancing is described as the special-case appropriate when the score-relevant error is covariate-only (arXiv:2605.06386).

Researchers building debiased estimators routinely rely on the Neyman orthogonal score because its orthogonality reduces sensitivity to first-stage nuisance estimation error. Industry-pattern observations: methodology papers that tie finite-dimensional balancing choices to the score often prompt reexamination of which basis functions practitioners include in balancing routines and how those bases interact with treatment heterogeneity.

Editorial analysis: For the causal-inference and DML communities, framing covariate balancing as a special case guided by the orthogonal score clarifies when simple covariate-based balancing is sufficient and when richer regressor bases are required. This distinction matters for empirical strategy selection, robustness checks, and simulation studies comparing ATE versus ATT targets.

Observers will look for follow-up work that:

• •provides empirical comparisons of covariate versus regressor balancing across heterogeneous-treatment settings
• •releases replication code that implements Riesz regression bases in common DML toolkits
• •connects theoretical conditions in the paper to finite-sample performance in applied datasets