Research map / Probabilistic and scientific modeling / Variational and generative sampling
On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Construct a piecewise-Hölder transport from a low-dimensional uniform source using local manifold charts | Deep ReLU generator · Distributions on a compact d-dimensional manifold | Wasserstein-1 approximation error: W_1((g_{\theta})_\sharp \rho, Q) < \epsilon | Helped |
| Use intrinsic dimension in the generator's statistical analysis | Deep Wasserstein learning (empirical risk minimizer) · Distributions on a compact d-dimensional manifold | Expected Wasserstein-1 estimation error: \mathbb{E} W_1((\hat{g}_n)_\sharp \rho, Q) \leq C n^{-\frac{1}{d+\delta}} | Helped |
| Train using noisy rather than clean samples | Deep Wasserstein learning · Noisy samples from distributions on a compact d-dimensional manifold | Expected Wasserstein-1 estimation error: C n^{-\frac{1}{d+\delta}} + 2\sqrt{V_\xi} | Hurt |
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