将瑞斯回归与密度比估计关联，提升因果推断的效率与灵活性。
Riesz Regression As Direct Density Ratio Estimation
- 利用瑞斯表示器等价于带符号密度比，建立新方法框架。
- 证明其目标函数与最小二乘重要性拟合一致，可直接复用现有理论。
- 适用于神经网络等复杂模型，支持快速收敛与正则化设计。
本研究厘清了瑞斯回归 [Chernozhukov et al., 2021] 与因果推断中密度比估计（DRE）之间的关系。我们首先证明瑞斯表示器可表示为带符号的密度比，进而表明瑞斯回归的目标函数等价于最小二乘重要性拟合准则 [Kanamori et al., 2009]。尽管瑞斯回归适用于广泛的表示器估计问题，但该等价性使得现有 DRE 的成果——包括收敛速率分析、基于 Bregman 散度最小化的推广，以及针对神经网络等灵活模型的正则化技术——均可直接迁移应用。
原文摘要 · Abstract (English)
This study clarifies the relationship between Riesz regression [Chernozhukov et al., 2021] and density ratio estimation (DRE) in causal inference problems, such as average treatment effect estimation. We first show that the Riesz representer can be written as a signed density ratio and then demonstrate that the Riesz regression objective coincides with the least-squares importance fitting criterion [Kanamori et al., 2009]. Although Riesz regression applies to a broad class of representer estimation problems, this equivalence with DRE allows us to transfer existing DRE results, including convergence rate analyses, generalizations based on Bregman divergence minimization, and regularization techniques for flexible models such as neural networks.
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