将最近邻匹配重新解释为最小二乘密度比估计，统一了因果推断方法。
Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression
- 用最小二乘法重释密度比估计，打通近邻匹配与统计建模的联系。
- 证明最近邻匹配本质是基于LSIF框架的最小二乘密度比估计。
- 为自动去偏机器学习提供理论支撑，适合因果推断研究者参考。
本研究证明最近邻（NN）匹配可被看作自动去偏机器学习中的瑞斯回归（Riesz regression）实例。Lin等（2023）提出一种新的密度比估计器，而Chernozhukov等（2024）发展了直接通过最小化均方误差来估计瑞斯表示元（即偏差校正项）的瑞斯回归方法。本文首先证明Lin等（2023）提出的密度比估计方法在本质上等价于Kanamori等（2009）提出的最小二乘重要性拟合（LSIF）。进一步，我们基于LSIF框架推导出瑞斯回归，并由此导出最近邻匹配。该工作基于作者2025a和2025b的研究成果。
原文摘要 · Abstract (English)
This study proves that Nearest Neighbor (NN) matching can be interpreted as an instance of Riesz regression for automatic debiased machine learning. Lin et al. (2023) shows that NN matching is an instance of density-ratio estimation with their new density-ratio estimator. Chernozhukov et al. (2024) develops Riesz regression for automatic debiased machine learning, which directly estimates the Riesz representer (or equivalently, the bias-correction term) by minimizing the mean squared error. In this study, we first prove that the density-ratio estimation method proposed in Lin et al. (2023) is essentially equivalent to Least-Squares Importance Fitting (LSIF) proposed in Kanamori et al. (2009) for direct density-ratio estimation. Furthermore, we derive Riesz regression using the LSIF framework. Based on these results, we derive NN matching from Riesz regression. This study is based on our work Kato (2025a) and Kato (2025b).
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