Research map / Learning theory and algorithms / Kernels and regression theory
On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Decrease regularization into the nearly interpolating regime | KRR with noisy observations · Noisy KRR, θ≥β | excess risk: Ω^{poly}_{P}(σ^2) | Hurt |
| Decrease regularization while observations are noiseless | KRR with noiseless observations · Noiseless KRR, θ increasing | excess risk: n^{-min(s,2)θ} | Helped |
| Use λ≈n^{-θ} with θ<β rather than θ≥β | KRR with noisy observations · Noisy KRR, θ<β | excess risk: Θ̃_P(n^{-min(s,2)θ} + σ^2 n^{-(1 - θ / β)}) | Helped |
| Add regularization to kernel interpolation | KRR with noiseless observations · Noiseless KRR | excess risk: O^{poly}_{P}(n^{-min(s,2)β}) | Hurt |
| Use kernel interpolation on noisy data | KRR · Noisy KRR | excess risk: Ω(σ^2) | Hurt |
| Increase regression-function smoothness beyond s=2 | KRR with regularization · Noisy and noiseless KRR | bias rate: n^{-min(s,2)θ} | No clear effect |
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