Training generative models from locally privatized data via entropic optimal transport
summary
Claim: entropic optimal transport lets a GAN trained only on locally privatized samples recover the raw data distribution rather than the noise-convolved one, provided the transport cost is matched to the privatization (L1 for Laplace, squared for Gaussian). Proof gives parametric rate (1/√n) statistical convergence that avoids the usual 1/n^{1/d} curse, with privacy ε appearing exponentially in constants. Experiments on a noisy half‑circle and MNIST (ε≈5) reconstruct the original manifold and digits.
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chapters (16)
- 0:00Introduction
- 1:05Differential privacy approaches
- 3:36Data-level privacy concept
- 6:10GAN framework
- 8:20Training GANs with privatized data
- 11:55Optimal transport variants
- 16:58Entropic optimal transport
- 18:23Modifying GANs with entropic regularization
- 20:33Convergence rates for GANs
- 23:06Curse of dimensionality in WGANs
- 24:30Faster convergence with entropic WGANs
- 28:51Theoretical bounds and assumptions
- 30:44Synthetic data experiments
- 32:11MNIST experiments and results
- 33:57Summary
- 34:19Comparison with central DP
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