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Generalized Riesz Regression

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Estimate a causal effect or a structural parameter with machine learning, and the term that removes the bias turns out to be a function called the Riesz representer. Generalized Riesz Regression estimates that representer by minimizing a Bregman divergence, and one theory then accounts for several methods that were proposed separately, covariate balancing and density-ratio estimation among them. The main paper is A Unified Framework for Debiased Machine Learning: Riesz Representer Fitting under Bregman Divergence (Kato, 2026, arXiv:2601.07752). The implementation is provided by genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression (Kato, 2026).

Problems addressed

Estimating a target parameter such as the average treatment effect with machine learning leaves the estimation error of the regression model behind as bias. Debiased machine learning cancels that bias by adding a correction term built from the Riesz representer, which pushes the difficulty one step back: the correction term itself has to be estimated. Riesz regression does it with squared distance and the tailored loss does it with the KL divergence, and until now the two have been treated as separate proposals. Generalized Riesz Regression reads the difference between them as a choice of Bregman divergence.

Two properties follow from that reading. When the divergence and the model are chosen together in the right way, the estimated representer matches the moments of the covariates on its own, which is automatic covariate balancing, and Neyman orthogonality holds without any estimate of the regression function, which is automatic Neyman orthogonalization. The second property also gives a way to sort out how debiased machine learning relates to targeted maximum likelihood estimation (TMLE). Density-ratio estimation has its own place inside the framework, and that connects this work to the line of research described on the Density-Ratio Estimation page.

Software: genriesz

genriesz is the Python package that implements the framework. You specify the functional you want to estimate, a model for the representer, and a Bregman divergence. The package then constructs the link function so that the balancing optimality condition holds, and runs estimation and statistical inference with cross-fitting. The documentation covers usage. Besides the average treatment effect, it handles the effect on the treated and marginal effects.

Research thread

2026
ScoreMatchingRiesz: Score Matching for Debiased Machine Learning and Policy Path Estimation (ICML 2026). Extends representer estimation to score matching.
2025
Riesz Regression As Direct Density Ratio Estimation. Shows that Riesz regression and density-ratio estimation are equivalent.
2025
Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression. Places nearest neighbor matching inside the framework.
2026
Covariate Balancing and Riesz Regression Should Be Guided by the Neyman Orthogonal Score in Debiased Machine Learning. Argues that the design of balancing and of Riesz regression should follow from the Neyman orthogonal score.
2026
Prediction-Powered Causal Inference by Automatic Debiased Machine Learning and Semi-Supervised Riesz Regression. Carries the framework over to causal inference that uses the output of a prediction model.
2025
Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation. Estimates the bias-correction term for the average treatment effect directly.

Relation to earlier work

Debiased machine learning, which estimates causal effects from machine learning fits and an orthogonal score, was established by Chernozhukov and coauthors (2018, Double/debiased machine learning for treatment and structural parameters). Riesz regression, which estimates the correction term directly as a regression, came out of the same group (2024, Automatic Debiased Machine Learning via Riesz Regression). Balancing the covariates directly instead of going through the propensity score has its best-known form in the covariate balancing propensity score of Imai and Ratkovic (2014, Covariate Balancing Propensity Score), and targeted maximum likelihood estimation (van der Laan and Rubin, 2006, Targeted Maximum Likelihood Learning) folds the correction into the estimator by another route. Generalized Riesz Regression lines these methods up along a single axis, the choice of Bregman divergence, and shows how they relate to one another.

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