The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.
Quantitative stability of optimal transport maps and linearization of the 2-wasserstein space
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Quantitative Stability of the Shadow for Wasserstein Projections and Sample Complexity
The shadow projection onto couplings is bi-Hölder continuous in Wasserstein distance, yielding explicit sample complexity rates for its estimation.