Research map / Probabilistic and scientific modeling / Variational and generative sampling
Statistical Regeneration Guarantees of the Wasserstein Autoencoder with Latent Space Consistency
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Constrain the encoded distribution to be within latent-space TV margin λ* of the target law | f-WAE · Latent space consistency | TV distance: \norm{\rho - \widehat{(E_{\#}\mu)}_{n}}_{TV} - \lambda^* \leq \frac{1}{\sqrt{n}}\Big\{c_1\sqrt{v} + c_2\sqrt{\ln{\big(\f | Helped |
| Use an encoder consistent in latent space and a decoder approximating a geometry-preserving transport map | f-WAE · Input distribution regeneration | Wasserstein distance: d_{\mathscr{L}^1_c}((D \circ E^*)_{\#}{\hat{\mu}_n}, {\mu}) - \zeta^* \leq \mathcal{O}(n^{-\frac{1}{s}}) + \mathcal{O}(n | Helped |
| Require an invertible decoder for transfer of the regeneration guarantee to the original WAE reconstruction loss | WAE · Input distribution regeneration | reconstruction loss: d^{*}_{c}(\hat{\mu}_n,(E^*,D)) - \zeta^* \leq \mathcal{O}(n^{-\frac{1}{s}}) + \mathcal{O}(n^{-\frac{1}{2}}) | Helped |
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