Research map / Learning theory and algorithms / Optimal transport
Asymptotic Guarantees for Generative Modeling Based on the Smooth Wasserstein Distance
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Gaussian-smoothed Wasserstein distance instead of classic Wasserstein distance | Empirical distribution estimation in arbitrary dimension · High-dimensional distributions | empirical convergence rate: $n^{-1/d}$ to $n^{-1/2}$ | Helped |
| Use smaller Gaussian smoothing parameter $\sigma$ | MSWE · Gaussian, d=5 and d=10 | limiting-distribution convergence | Hurt |
| Use smaller Gaussian smoothing parameter $\sigma$ | SWD GAN · 10D Gaussian mixture | SWD convergence rate | Hurt |
| Increase the number of samples | MSWE · 1D Gaussian mixture | limiting-distribution convergence: 16-fold increase in $n$ | Helped |
| Increase the number of samples | MSWE · Gaussian, d=5 and d=10 | limiting-distribution convergence | Helped |
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