A common goal in observational research is to estimate marginal causal effects in the presence of confounding variables. One solution to this problem is to use the covariate distribution to weight the outcomes such that the data appear randomized. The propensity score is a natural quantity that arises in this setting. Propensity score weights have desirable asymptotic properties, but they often fail to adequately balance covariate data in finite samples. Empirical covariate balancing methods pose as an appealing alternative by exactly balancing the sample moments of the covariate distribution. With this objective in mind, we propose a framework for estimating balancing weights by solving a constrained convex program, where the criterion function to be optimized is a Bregman distance. We then show that the different distances in this class render identical weights to those of other covariate balancing methods. A series of numerical studies are presented to demonstrate these similarities.

中文翻译：

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使用 Bregman 距离的协变量平衡框架

观察性研究的一个共同目标是在存在混杂变量的情况下估计边际因果效应。该问题的一种解决方案是使用协变量分布对结果进行加权，使数据看起来是随机的。倾向得分是在这种情况下出现的自然量。倾向得分权重具有理想的渐近特性，但它们通常无法充分平衡有限样本中的协变量数据。通过精确平衡协变量分布的样本矩，经验协变量平衡方法是一种有吸引力的替代方法。考虑到这一目标，我们提出了一个通过求解约束凸程序来估计平衡权重的框架，其中要优化的标准函数是 Bregman 距离。然后我们表明，此类中的不同距离呈现与其他协变量平衡方法相同的权重。提出了一系列数值研究来证明这些相似性。