# Sinkhorn Treatment Effects: A Causal Optimal Transport Measure

arXiv: https://arxiv.org/abs/2605.08485 · HTML: https://mlsanity.com/paper/2605.08485/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 82 references that are in the map.
- First posted on arXiv 8 May 2026.

## Builds on (most cited first, 3 of 3)

- [A survey of the Schr"odinger problem and some of its connections with optimal transport](https://mlsanity.com/paper/1308.0215/) (2013)
- [The Riemannian geometry of Sinkhorn divergences](https://mlsanity.com/paper/2405.04987/) (2024)
- [Coreset selection for the Sinkhorn divergence and generic smooth divergences](https://mlsanity.com/paper/2504.20194/) (2025)

## Built on by (most cited first, 1 of 1)

- [Semiparametrically Efficient Inference for Kernel Measures of Noise Heterogeneity](https://mlsanity.com/paper/2605.27526/) (2026)

## Abstract (arXiv)

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.