提出统一框架，用广义瑞斯回归实现无偏机器学习。
Generalized Riesz Regression: A Unified Framework for Debiased Machine Learning with Riesz Representer Fitting under Bregman Divergence
- 基于瑞斯恒等式最小化可观测的Bregman散度，统一多种无偏学习方法。
- 在双可微生成器下，首次阶条件给出模型相关的瑞斯方程，控制系统性误差。
- 适用于处理效应、边际效应等场景，对稀疏模型和神经网络有收敛率保证。
估计瑞斯表示是实现无偏机器学习的核心，但生成器与表示模型决定了其一阶条件保护的回归方向。本文提出广义瑞斯回归，通过瑞斯恒等式将可观测的Bregman散度最小化。平方与Kullback-Leibler型选择分别恢复瑞斯回归、定制损失最小化及密度比目标。对于任意二阶可微生成器与可微表示模型，一阶条件在模型相关的切向方向上诱导出经验瑞斯方程。兼容性使这些方向与预先选定的回归变量对齐。该方程在精确平衡下给出系统性奈曼误差的紧致控制，并满足正交得分恒等式。我们推导了稀疏模型（线性于对偶坐标）、再生核希尔伯特空间模型及神经网络的收敛速率，其中生成器曲率影响稀疏模型的速率。在多斯克条件或通过交叉拟合进行异质性估计时，建立了渐近正态性。应用涵盖处理效应、平均边际效应与协变量偏移。
原文摘要 · Abstract (English)
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.
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