Research map / Learning theory and algorithms / Optimal transport
Monge, Bregman and Occam: Interpretable Optimal Transport in High-Dimensions with Feature-Sparse Maps
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use STVS instead of the ℓ1 regularizer | Generalized entropic transport maps · Synthetic constant sparsity-pattern task | NMSE | Helped |
| Use sparsity-inducing elastic costs instead of the squared-ℓ2 cost | Generalized entropic transport maps · Synthetic input-dependent sparsity-pattern task | NMSE scaling with dimension | Helped |
| Increase sparsity of the displacement maps | Elastic-ℓ1 transport maps · Single-cell perturbation data | ℓ₂²-Sinkhorn divergence in PCA space | No clear effect |
| Induce sparsity in displacements | Elastic-ℓ1 transport maps · Single-cell perturbation data, low drug dosages | R² on marker genes | Helped |
| Induce sparsity in displacements | Elastic-ℓ1 transport maps · Single-cell perturbation data, high drug dosages | R² on marker genes | Mixed |
| Use sparse maps to select marker genes | Generalized entropic transport maps · Single-cell perturbation data | Ranked biased overlap | Helped |
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