Weighting methods in causal inference have been widely used to achieve a desirable level of covariate balancing. However, the existing weighting methods have desirable theoretical properties only when a certain model, either the propensity score or outcome regression model, is correctly specified. In addition, the corresponding estimators do not behave well for finite samples due to large variance even when the model is correctly specified. In this paper, we consider to use the integral probability metric (IPM), which is a metric between two probability measures, for covariate balancing. Optimal weights are determined so that weighted empirical distributions for the treated and control groups have the smallest IPM value for a given set of discriminators. We prove that the corresponding estimator can be consistent without correctly specifying any model (neither the propensity score nor the outcome regression model). In addition, we empirically show that our proposed method outperforms existing weighting methods with large margins for finite samples.

翻译：在因果推断中，加权方法已被广泛用于实现理想的协变量平衡水平。然而，现有加权方法仅在特定模型（倾向性评分模型或结果回归模型）被正确设定时才具有理想的统计性质。此外，即使模型设定正确，对应估计量在有限样本下也因方差过大而表现不佳。本文考虑利用积分概率度量——一种衡量两个概率分布之间差异的指标——进行协变量平衡。通过优化权重使得处理组和对照组加权后的经验分布在给定判别函数集上具有最小的积分概率度量值，我们证明了即使无需正确设定任何模型（既不需要倾向性评分模型也不需要结果回归模型），对应估计量仍可具备相合性。此外，实证结果表明，在有限样本下，我们提出的方法在性能上显著优于现有加权方法。