Research map / Optimization / Nonconvex and smooth optimization
Continuous Regularized Wasserstein Barycenters
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use continuous-support barycenter optimization with quadratic regularization | Wasserstein barycenter computation · Multivariate Gaussians, dimensions 4–8 | covariance difference: dimension 4: 1.22{\times 10^{-2}}(1.44{\times 10^{-3}}); dimension 5: 1.52{\times 10^{-2}}(1.18{\times 10^{-3}}); dimens | Helped |
| Use continuous-support barycenter optimization with quadratic regularization | Wasserstein barycenter computation · Multivariate Gaussians, dimensions 2–3 | covariance difference: dimension 2: 1.98{\times 10^{-3}}(1.17{\times 10^{-4}); dimension 3: 5.05{\times 10^{-3}}(6.32{\times 10^{-4}) | Mixed |
| Use continuous-support barycenter optimization with quadratic regularization | Wasserstein barycenter computation · BikeTrips subset posterior aggregation | covariance difference: 2.43{\times 10^{-7}}(6.57 {\times 10^{-8}) versus 2.56{\times 10^{-7}}(2.17{\times 10^{-9}) | Helped |
| Replace quadratic regularization with entropic regularization (ablation) | Ours · Multivariate Gaussians, dimensions 2–8 | covariance difference: dimension 2: 1.98{\times 10^{-3}}(1.17{\times 10^{-4}) -> 8.25 \times 10^{-3}(5.02 \times 10^{-4}); dimension 8: 4.23{\t | Hurt |
| Use an alternate Monge map estimation method (ablation) | Ours · Multivariate Gaussians, dimensions 2–8 | covariance difference: dimension 2: 1.98{\times 10^{-3}}(1.17{\times 10^{-4}) -> 2.38{\times 10^{-3}}(2.48{\times 10^{-4}) | Hurt |
| Use random Fourier features instead of neural networks for potential parameterization (ablation) | Ours · Digit 3 synthetic barycenter | qualitative barycenter quality | No clear effect |
| Decrease the regularization parameter (ablation) | Ours · Digit 3 synthetic barycenter | barycenter sharpness | Helped |
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