最近邻匹配作为最小二乘密度比估计与Riesz回归 (Nearest Neighbor Matching as Least Squares Density Ratio Estimation and Riesz Regression)

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).

翻译：本研究证明最近邻（NN）匹配可被解释为自动去偏机器学习中Riesz回归的一个实例。Lin等人（2023）通过其新提出的密度比估计器表明，NN匹配是一种密度比估计方法。Chernozhukov等人（2024）发展了用于自动去偏机器学习的Riesz回归，该方法通过最小化均方误差直接估计Riesz表示子（即偏置校正项）。在本研究中，我们首先证明Lin等人（2023）提出的密度比估计方法本质上等同于Kanamori等人（2009）为直接密度比估计提出的最小二乘重要性拟合（LSIF）。进一步地，我们基于LSIF框架推导出Riesz回归。基于这些结果，我们从Riesz回归推导出NN匹配。本研究基于我们的工作Kato（2025a）和Kato（2025b）。