Research map / Learning theory and algorithms / Kernels and regression theory
Comparing distributions: $\ell_1$ geometry improves kernel two-sample testing
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Optimize test locations and Gaussian width rather than use randomly drawn locations with grid-searched width (ablation) | L1-ME · Fast food: McDo vs Burger King | Type-II error: 0.426 -> 0.112 | Helped |
| Optimize test locations and Gaussian width rather than use randomly drawn locations with grid-searched width (ablation) | L1-SCF · Fast food: McDo vs Burger King | Type-II error: 0.960 -> 0.428 | Helped |
| Use L1 geometry instead of the L2 mean-embedding test | Mean-embedding two-sample test · Fast food: McDo vs Wendy's | Type-II error: 0.416 -> 0.156 | Helped |
| Optimize test locations and Gaussian width rather than use randomly drawn locations with grid-searched width (ablation) | L1-SCF · Fast food: McDo vs Arby's | Type-II error: 0.468 -> 0.006 | Helped |
| Optimize test locations and Gaussian width rather than use randomly drawn locations with grid-searched width (ablation) | L1-ME · Fast food: McDo vs Taco Bell | Type-II error: 0.624 -> 0.554 | Helped |
| Use L1 geometry rather than L2 geometry | Kernel two-sample tests · Synthetic GMD, GVD, and Blobs | test power | Helped |
| Optimize test locations rather than use random locations (ablation) | L1-ME and L1-SCF · Synthetic GMD, GVD, and Blobs | test power | Helped |
| Use SCF features instead of mean-embedding features | L1 test · Synthetic Blobs | test power | Helped |
| Use L1-opt-SCF instead of quadratic-time MMD | Two-sample test · Synthetic GVD | test power | Helped |
| Use L1-opt-SCF instead of quadratic-time MMD | Two-sample test · Synthetic Blobs | test power | Helped |
| Use optimized L1 tests rather than their L2 counterparts | Kernel two-sample test · Higgs | Type-II error | Helped |
| Optimize locations rather than use grid-based random locations (ablation) | L1-ME and L1-SCF · Higgs | Type-II error | Helped |
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