用熵正则最优传输衡量处理效应分布差异，提升因果推断精度。
Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
- 基于熵正则最优传输构建处理效应新度量，捕捉全分布差异。
- 提出无偏估计器与渐近有效检验，支持固定正则化参数下的统计推断。
- 设计多参数聚合检验，提升实际应用中对未知参数的鲁棒性。
我们引入了Sinkhorn处理效应，一种基于熵正则最优传输的反事实分布差异度量。与传统平均处理效应不同，该度量能刻画整个分布的差异。我们将其视为统计函数，并证明其可表示为反事实均值嵌入的平滑变换（在适当核函数下）。这一表征使我们建立了一阶路径可微性，且在反事实分布相等的零假设下具备二阶路径可微性。利用此光滑性，我们构造了无偏估计器，并据此获得固定熵正则化参数下的渐近有效分布处理效应检验。由于检验功效依赖于未知正则化参数，我们进一步提出在一组正则化选择上聚合证据的综合检验方法。模拟数据与图像数据实验验证了该估计器与检验程序的实际优势。
原文摘要 · Abstract (English)
We introduce the Sinkhorn treatment effect, an entropic optimal transport measure of divergence between counterfactual distributions. Unlike classical quantities such as the average treatment effect, this measure captures differences across entire distributions. We analyze this divergence as a statistical functional and show it can be written as a smooth transformation of counterfactual mean embeddings with an appropriate kernel. This characterization allows us to establish first-order pathwise differentiability in general, and second-order pathwise differentiability under the null hypothesis of equal counterfactual distributions. Leveraging this smoothness, we construct debiased estimators and use them to obtain asymptotically valid tests for distributional treatment effects with a fixed entropic regularization parameter. Because the power of the test depends on this unknown parameter, we further propose an aggregated test that combines evidence across a grid of regularization choices. Experiments on simulated and image data demonstrate the practical advantages of our estimator and testing procedure.
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