Research map / Learning theory and algorithms / Kernels and regression theory
Kernel Quadrature with Randomly Pivoted Cholesky
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use RPCholesky node sampling instead of continuous volume sampling | Kernel quadrature · Sobolev space H^s_per([0,1]), s = 3, d = 1, n = 128 | sampling time: 17× faster | Helped |
| Use RPCholesky node sampling instead of kernel thinning | Kernel quadrature · Sobolev space H^s_per([0,1]), s = 3, d = 1, n = 128 | sampling time: 52× faster | Helped |
| Use RPCholesky node sampling instead of PWKQ | Kernel quadrature · Sobolev space H^s_per([0,1]), s = 3, d = 1, n = 128 | sampling time: 170× faster | Helped |
| Use RPCholesky nodes instead of IID or Monte Carlo sampling | Kernel quadrature on QM9 · QM9 isotropic polarizability, sufficiently large n | mean relative error: a factor of three at n=512 | Helped |
| Use optimized rejection sampling to update the acceptance bound (ablation) | RPCholesky sampling · [0,1]^3, n = 200 | sampling time: 7.47 -> 0.19 seconds | Helped |
| Use RPCholesky rather than IID sampling | Kernel quadrature · QM9 worst-case quadrature error | worst-case quadrature error | Helped |
| Use RPCholesky rather than continuous volume sampling | Kernel quadrature · Periodic Sobolev benchmark | quadrature error | No clear effect |
Closest papers by meaning
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- An analysis of Ermakov-Zolotukhin quadrature using kernels (NeurIPS 2021 · similarity 0.85)
- Fast Summation of Radial Kernels via QMC Slicing (ICLR 2025 · similarity 0.82)
- Random features for Grassmannian kernel approximation with bounded rank-one projections (NeurIPS 2026 · similarity 0.80)
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