统一因果推断框架，用双曲回归实现无偏估计。
A Unified Theory for Causal Inference: Direct Debiased Machine Learning via Bregman-Riesz Regression
- 以双曲-瑞斯回归为核心，整合多种权重估计方法
- 匹配与密度比估计在均值处理效应下等价
- 适合需要无偏因果估计的研究者
本文提出一个统一的因果推断理论，将瑞斯回归、协变量平衡、密度比估计（DRE）、目标最大似然估计（TMLE）和匹配估计器整合于平均处理效应（ATE）估计中。在ATE估计中，平衡权重与结果回归函数至关重要，平衡权重可称为瑞斯表示子、偏差校正项或聪明协变量。瑞斯回归、协变量平衡、DRE及匹配估计器均用于估计平衡权重，其中瑞斯回归在ATE背景下等价于DRE，匹配估计器是DRE的特例，且DRE与协变量平衡存在对偶关系。TMLE是一种构建回归函数估计量的方法，使主要偏差项为零。最近邻匹配等价于最小二乘密度比估计与瑞斯回归。
原文摘要 · Abstract (English)
This note introduces a unified theory for causal inference that integrates Riesz regression, covariate balancing, density-ratio estimation (DRE), targeted maximum likelihood estimation (TMLE), and the matching estimator in average treatment effect (ATE) estimation. In ATE estimation, the balancing weights and the regression functions of the outcome play important roles, where the balancing weights are referred to as the Riesz representer, bias-correction term, and clever covariates, depending on the context. Riesz regression, covariate balancing, DRE, and the matching estimator are methods for estimating the balancing weights, where Riesz regression is essentially equivalent to DRE in the ATE context, the matching estimator is a special case of DRE, and DRE is in a dual relationship with covariate balancing. TMLE is a method for constructing regression function estimators such that the leading bias term becomes zero. Nearest Neighbor Matching is equivalent to Least Squares Density Ratio Estimation and Riesz Regression.
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