aiqbench analysis
This paper advances debiased machine learning by introducing generalized Riesz regression, which unifies various loss functions under a Bregman divergence framework to improve estimation accuracy. By deriving convergence rates for diverse architectures including neural networks and reproducing kernel Hilbert spaces, the work provides rigorous theoretical guarantees for causal inference tasks like treatment effect estimation.
Generalized Riesz Regression: A Unified Framework for Debiased Machine Learning with Riesz Representer Fitting under Bregman Divergence
arXiv:2601.07752v4 Announce Type: replace-cross 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.
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.
Econometrics (econ.EM); Machine Learning (cs.LG); Statistics Theory (math.ST); Methodology (stat.ME); Machine Learning (stat.ML)
arXiv:2601.07752 [econ.EM]
(or arXiv:2601.07752v4 [econ.EM] for this version)
https://doi.org/10.48550/arXiv.2601.07752 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 248 words
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