Research map / Learning theory and algorithms / Kernels and regression theory
Improved Convergence Rates for Sparse Approximation Methods in Kernel-Based Learning
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use sparse approximate statistics with uncertainty-reduction data selection | Kernel regression · Finite-domain regression | uniform prediction error: \mathcal{O}\left(\sqrt{\frac{\gamma_k(n)}{n}\log\Big(\frac{|\mathcal{X}|}{\delta}\Big)}\right) | Helped |
| Use sparse approximate statistics with uncertainty-reduction data selection | Kernel regression · Compact-domain regression | uniform prediction error: \mathcal{O}\left(\sqrt{\frac{d\gamma_k(n)}{n}\log\Big(\frac{n}{\delta}\Big)}\right) | Helped |
| Replace exact GP statistics in BPE with sparse approximate statistics | BPE · Kernel bandit optimization | cumulative regret: \Oct\left(\sqrt{N\gamma_k(N)\log\Big(\frac{|\mathcal{X}|}{\delta}\Big)}\right); \Oct(\gamma_k(N)\sqrt{N}) | Helped |
| Use S-BPE instead of BKB or S-GP-TS | Kernel bandit optimization · Matérn kernels | regret rate: \Oct\left(N^{\frac{\nu+d}{2\nu+d}}(\log(N))^{\frac{\nu}{2\nu+d}}\sqrt{d\log\Big(\frac{N}{\delta}\Big)}\right); \Oct(N^{\ | Helped |
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