Debiased Machine Learning and Riesz Regression

• debiased machine learning
• Riesz representer
• Neyman orthogonality
• semiparametrics

The question

Plug a flexible machine learning fit into a causal estimand and the regularization that made the fit possible leaves a first-order bias behind. Debiased machine learning removes it with a Neyman-orthogonal score whose correction term is built from the Riesz representer of the target functional — inverse propensity weights for the average treatment effect, and their analogues elsewhere.

So the accuracy of the whole procedure is inherited from the quality of the representer estimate. Several methods exist for that step — Riesz regression, tailored loss minimization, covariate balancing, density ratio fitting — developed separately, with separate justifications. Are they instances of one thing?

A unified answer

Generalized Riesz regression estimates the representer by minimizing a Bregman divergence. Squared distance recovers Riesz regression; KL divergence recovers tailored loss minimization; other divergences give new estimators. Two properties follow from the structure rather than being imposed:

• Automatic covariate balancing — for suitable divergence and link pairs, the dual of the fitting problem is a covariate balancing problem.
• Automatic Neyman orthogonalization — the representer-weighted outcome average is Neyman orthogonal without estimating the regression function, which also marks a concrete difference between debiased machine learning and targeted maximum likelihood estimation.

Convergence is analyzed for RKHS and neural network classes, and the framework is released as the genriesz Python package.

Related threads

• ScoreMatchingRiesz (ICML 2026) estimates the representer by score matching and applies it to policy path estimation.
• Importance weighting for conditional moment restrictions (ICLR 2022, spotlight) makes nonparametric instrumental variable estimation tractable with flexible models.
• Double debiased covariate shift adaptation (arXiv:2310.16638) makes covariate shift correction robust to error in the density ratio estimate itself.
• A technical note on the doubly robust estimator in regression discontinuity designs (arXiv:2411.07978).

Software

genriesz — specify the target functional, the representer model, and the Bregman divergence; the package constructs the link function, cross-fits, and returns estimates with inference for average treatment effects, treatment-specific means, and marginal effects. GitHub · Documentation