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.

翻译：本研究阐明了Riesz回归[Chernozhukov等，2021]与因果推断问题（如平均处理效应估计）中密度比估计（DRE）之间的关系。我们首先证明了Riesz表示子可被写为有符号密度比，进而展示了Riesz回归目标与最小二乘重要性拟合准则[Kanamori等，2009]的一致性。尽管Riesz回归适用于广泛类别的表示子估计问题，但与DRE的这种等价性使我们能够移植现有的DRE研究成果，包括收敛率分析、基于Bregman散度最小化的泛化方法，以及针对神经网络等灵活模型的正则化技术。