Research map / Learning theory and algorithms / Optimal transport
Gromov-Wasserstein Averaging of Kernel and Distance Matrices
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| GW distance on raw Coulomb matrices with 3-NN instead of Euclidean k-NN | k-nearest neighbors · qm7 atomization energy | MAE: 71.54 -> 10.83 | Helped |
| GW 3-NN vs linear regression | linear regression · qm7 atomization energy | MAE: 20.72 -> 10.83 | Helped |
| GW 3-NN vs Gaussian kernel ridge regression | kernel ridge · qm7 atomization energy | MAE: 8.57 -> 10.83 | Hurt |
| GW 3-NN vs Laplacian kernel ridge regression (8 copies) | kernel ridge · qm7 atomization energy | MAE: 3.07 -> 10.83 | Hurt |
| GW 3-NN vs multilayer neural network (1000 copies) | neural net · qm7 atomization energy | RMSE: 5.96 -> 29.27 | Hurt |
| avoid permuted copies by using unpadded Coulomb matrices directly with GW | Coulomb matrix representation · qm7 atomization energy | MAE: 71.54 -> 10.83 | Helped |
| increase entropic regularization epsilon in GW barycenter (ablation) | GW barycenter shape embedding · shape barycenters | qualitative | Mixed |
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