Research map / Learning theory and algorithms / Kernels and regression theory
Kernel Methods Through the Roof: Handling Billions of Points Efficiently
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use float32 precision instead of float64 (ablation) | Falkon · HIGGS | preconditioner / iteration time: 2337 s -> 1306 s; 4565 s -> 1496 s | Helped |
| move preconditioner to GPU (ablation) | Falkon · HIGGS | preconditioner time: 1306 s -> 179 s | Helped |
| use 2 GPUs instead of 1 (ablation) | Falkon · HIGGS | iteration time: 1344 s -> 693 s | Helped |
| use KeOps for thin blocks matrix-vector products (ablation) | Falkon · HIGGS | iteration time: 693 s -> 232 s | Helped |
| all GPU optimizations vs original Falkon (ablation) | Falkon · HIGGS | time: 19.7x preconditioner, 18.8x iterations | Helped |
| Falkon vs GPyTorch/GPflow SVGP on TAXI | Falkon · TAXI | RMSE and time: 311.7 vs 315.0, 3628 s vs 37009 s | Helped |
| logistic loss (LogFalkon) instead of squared loss (ablation) | Falkon · HIGGS | 1 - AUC: 0.1804 -> 0.1787 | Helped |
| logistic loss (LogFalkon) instead of squared loss (ablation) | Falkon · HIGGS | time (s): 443 -> 2267 | Hurt |
| use low-precision floats vs original Falkon | Falkon · HIGGS | error | Hurt |
| single GPU instead of two GPUs (ablation) | Falkon · large datasets | running time: 1.6x slower on average | Hurt |
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