Generalized Riesz Regression: A Unified Framework for Debiased Machine Learning with Riesz Representer Fitting under Bregman Divergence
econ.EM, cs.LG, math.ST, stat.ME, stat.ML, stat.TH
Submitted: 2026-01-12
Updated: 2026-08-25
Code: https://github.com/MasaKat0/genriesz
Project page: https://alejandroschuler.github.io/mci
License: http://creativecommons.org/licenses/by-nc-nd/4.0/
The gist: Estimating the Riesz representer is central to debiased machine learning, yet the generator and representer model determine which regression directions their first-order conditions protect.
Terminology
Abstract
Estimating the Riesz representer is central to debiased machine learning, yet the generator and representer model determine which regression directions their first-order conditions protect. We introduce generalized Riesz regression, which minimizes a Bregman divergence made observable by the Riesz identity. Squared and Kullback--Leibler-type choices recover Riesz regression, tailored loss minimization, and density-ratio objectives. For any twice-differentiable generator and differentiable representer model, the first-order conditions impose empirical Riesz equations in model-dependent tangent directions. Compatibility aligns those directions with regressors chosen in advance. These equations give sharp control of the systematic Neyman error and an orthogonal-score identity under exact balance. We derive convergence rates for sparse models linear in dual coordinates, reproducing kernel Hilbert space models, and neural networks, with generator curvature entering the sparse rate. We establish asymptotic normality under Donsker conditions or nuisance estimation via cross-fitting. Applications include treatment effects, average marginal effects, and covariate shift.
Sources
- Direct Bias-Correction Term Estimation for Average Treatment Effect Estimation
- A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression
- Direct Debiased Machine Learning via Bregman Divergence Minimization
- The Balancing Act in Causal Inference
- Automatic Debiased Machine Learning via Riesz Regression
- Automatic Debiased Machine Learning for Covariate Shifts
- Direct Density Ratio Optimization: A Statistically Consistent Approach to Aligning Large Language Models
- Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression
- Riesz Regression As Direct Density Ratio Estimation
- ScoreMatchingRiesz: Score Matching for Debiased Machine Learning and Policy Path Estimation
- Semi-Supervised Treatment Effect Estimation with Unlabeled Covariates for Prediction-Powered Causal Inference
- Double Debiased Covariate Shift Adaptation Robust to Density-Ratio Estimation
- PUATE: Efficient Average Treatment Effect Estimation from Treated (Positive) and Unlabeled Units
- RieszBoost: Gradient Boosting for Riesz Regression
- Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency
- General Bayesian inference for causal effects using covariate balancing procedure
- Distributional Balancing for Causal Inference: A Unified Framework via Characteristic Function Distance
- Kernel Ridge Riesz Representers: Generalization, Mis-specification, and the Counterfactual Effective Dimension
- Generative Modeling by Estimating Gradients of the Data Distribution
- Likelihood-free inference by ratio estimation
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