Research map / Learning theory and algorithms / Optimal transport
Distributional Convergence of the Sliced Wasserstein Process
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a uniform central limit theorem for projected empirical Wasserstein distances and apply regular functionals to the process | Sliced Wasserstein distance and its variants · Compactly supported distributions with connected projections | distributional convergence | Helped |
| Increase sample size | Empirical sliced Wasserstein · Uniform unit sphere vs. shifted unit sphere | approximation to limiting Gaussian distribution | Helped |
| Use the naive bootstrap rather than fewer bootstrap replacements | Empirical sliced Wasserstein · Uniform unit sphere vs. shifted unit sphere | bootstrap approximation to finite-sample distribution | Helped |
| Use different bootstrap replacement counts | Empirical max-sliced Wasserstein · Uniform sphere vs. ellipsoid with a = 8.5 | bootstrap approximation | No clear effect |
| Increase sample size | Empirical max-sliced Wasserstein · Uniform sphere vs. ellipsoid with a = 8.5 | approximation to limiting Gaussian distribution | Helped |
| Use a smaller bootstrap sample with k → ∞ and k/n → 0 | Sliced Wasserstein functionals with directionally Hadamard differentiable F · Compactly supported distributions with connected projections | bootstrap consistency | Helped |
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