Research map / Learning theory and algorithms / Kernels and regression theory
Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| sample Fourier features from an upper bound on the ridge leverage function instead of the classic Fourier density | Kernel ridge regression with shift-invariant kernels · Spectral approximation of the regularized kernel matrix | number of Fourier features required: s = O(s_λ(K) log(s_λ(K))) | Helped |
| use classic Fourier-density sampling rather than ridge-leverage-based sampling | Kernel ridge regression with the Gaussian kernel · Spectral approximation, including bounded datasets in the lower-bound construction | number of Fourier features required: s=Ω(n_λ / 2^{O(d)}); s=Ω(n_λ) | Hurt |
| cap low-frequency sampling mass and allocate more samples to higher frequencies using the improved Gaussian-kernel distribution | Gaussian-kernel random Fourier features · Spectral approximation for datasets in an ℓ∞-ball of radius R | number of Fourier features required: s_{\bar{\tau}_R} = O\Big( (248R)^d \log(n_\lambda)^{d/2} + (200\log n_\lambda)^{2d}\Big) | Helped |
Closest papers by meaning
- Towards a Unified Analysis of Random Fourier Features (ICML 2019 · similarity 0.90)
- A random matrix analysis of random Fourier features: beyond the Gaussian kernel, a precise phase transition, and the corresponding double descent (NeurIPS 2020 · similarity 0.90)
- Learning Adaptive Random Features (AAAI 2019 · similarity 0.90)
- Fourier Sparse Leverage Scores and Approximate Kernel Learning (NeurIPS 2020 · similarity 0.90)
- A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regression (NeurIPS 2024 · similarity 0.88)
- Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms (NeurIPS 2024 · similarity 0.87)
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