Research map / Learning theory and algorithms / Kernels and regression theory
Failure and success of the spectral bias prediction for Laplace Kernel Ridge Regression: the case of low-dimensional data
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's title only (no summary yet). Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the spectral-bias prediction for the ridgeless test-error exponent | Laplace KRR with data density vanishing at the decision boundary · 1D synthetic, vanishing ridge | test error scaling: \varepsilon_t \sim P^{-1+\left(\frac{2\xi}{\chi+1}\right)}; \varepsilon_B\sim P^{-1-\left(\frac{\chi-4\xi}{\chi+2}\right | Hurt |
| Increase the ridge above the crossover scale | Laplace KRR and replica-method prediction · 1D synthetic | agreement with empirical test error: \lambda^*_{1,\chi}\sim P^{-\frac{1}{1+\chi}} | Helped |
| Use the spectral-bias prediction when the boundary density is nonvanishing (\chi=0) | Laplace KRR · d-dimensional synthetic, ridgeless | test error exponent | Helped |
| Use the spectral-bias prediction at finite dimension when boundary density vanishes (\chi>0) | Laplace KRR · d-dimensional synthetic, ridgeless | test error exponent | Hurt |
| Increase dimension toward the high-dimensional limit | Laplace KRR with vanishing boundary density · d-dimensional synthetic, ridgeless | test error exponent agreement: d\rightarrow \infty | Helped |
| Raise the ridge above the crossover scale | Laplace KRR and replica-method prediction · d-dimensional synthetic | agreement with empirical test error: \lambda^*_{d,\chi}\sim P^{-\frac{1}{d+\chi}} | Helped |
| Apply the decision-boundary density model with d=35 and \chi=1.5 | Laplace KRR · Binary CIFAR-10 | test error versus ridge fit: d=35 and \chi=1.5 | Helped |
Closest papers by meaning
- A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression (NeurIPS 2024 · similarity 0.90)
- Overfitting Behaviour of Gaussian Kernel Ridgeless Regression: Varying Bandwidth or Dimensionality (NeurIPS 2024 · similarity 0.88)
- Characterizing Overfitting in Kernel Ridgeless Regression Through the Eigenspectrum (ICML 2024 · similarity 0.88)
- Generalization error of spectral algorithms (ICLR 2024 · similarity 0.87)
- Kernel Regression in Structured Non-IID Settings: Theory and Implications for Denoising Score Learning (NeurIPS 2025 · similarity 0.87)
- On the Saturation Effects of Spectral Algorithms in Large Dimensions (NeurIPS 2024 · similarity 0.87)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.