The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
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Explicit closed-form solution for static KL-unbalanced OT between non-degenerate Gaussians with quadratic cost and two-sided marginal relaxations, without coupling entropy; minimizer is scaled Wasserstein coupling of adjusted marginals supported on affine graph with covariance solving Riccati.
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Sinkhorn Treatment Effects: A Causal Optimal Transport Measure
The Sinkhorn treatment effect is a new entropic optimal transport measure of divergence between counterfactual distributions that admits first- and second-order pathwise differentiability, debiased estimators, and asymptotically valid tests for distributional treatment effects.
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Closed Forms for Gaussian Kullback--Leibler Unbalanced Optimal Transport without Coupling Entropy
Explicit closed-form solution for static KL-unbalanced OT between non-degenerate Gaussians with quadratic cost and two-sided marginal relaxations, without coupling entropy; minimizer is scaled Wasserstein coupling of adjusted marginals supported on affine graph with covariance solving Riccati.