Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
For causal inference researchers, this provides a new tool for testing distributional treatment effects beyond average effects, though the contribution is incremental as it builds on existing optimal transport and causal inference frameworks.
The paper introduces the Sinkhorn treatment effect, an entropic optimal transport measure for comparing counterfactual distributions, and develops debiased estimators and asymptotically valid tests for distributional treatment effects. Experiments on simulated and image data demonstrate practical advantages.
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.