Research map / Learning theory and algorithms / Kernels and regression theory
Sharp Analysis of Random Fourier Features in Classification
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the regularity condition f_H = L^r g with r ∈ [1/2,1] in the analysis | RFF classification · Lipschitz-loss classification, O(1/√n) learning rate | number of features: Ω(n) -> Ω(√n log n) | Helped |
| Use ridge leverage score sampling instead of plain spectral-measure sampling | RFF classification · O(1/√n), finite-rank spectrum | number of features: s ∈ Ω (n^{1/2r}) -> s ∈ Ω(1) | Helped |
| Use ridge leverage score sampling instead of plain spectral-measure sampling | RFF classification · O(1/√n), polynomial spectrum μ_i ∝ i^{-2γ}, γ ≥ 1 | number of features: s ∈ Ω (n^{1/2γ} · log n) -> s ∈ Ω (n^{1/4γr} · log n) | Helped |
| Use ridge leverage score sampling instead of plain spectral-measure sampling | RFF classification · O(1/√n), μ_i ∝ i^{-1} | number of features: s ∈ Ω (n · log n) -> s ∈ Ω (n^{1/2r} · log n) | Helped |
| Apply the regularity condition to plain RFF | Plain RFF classification · Worst case r = 1/2 | computational savings | No clear effect |
| Assume Massart's low-noise condition | Plain and leverage-weighted RFF classification · Finite-rank spectrum | learning rate: O(1/√n) -> O(1/n) | Helped |
| Use leverage-weighted RFF for the fast-rate setting | RFF classification · O(1/n), finite-rank spectrum | number of features: s ∈ Ω(n^{1/r}) -> s ∈ Ω(1) | Helped |
| Use leverage-weighted RFF for the fast-rate setting | RFF classification · Exponential spectrum, O(log n / n) rate | number of features: s ∈ Ω(n^{1/r}) -> s ∈ Ω (log n · log log n) | Helped |
Closest papers by meaning
- Towards a Unified Analysis of Random Fourier Features (ICML 2019 · similarity 0.93)
- Learning Adaptive Random Features (AAAI 2019 · similarity 0.91)
- 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)
- Large-Scale Learning with Fourier Features and Tensor Decompositions (NeurIPS 2021 · similarity 0.89)
- Efficiently Learning Significant Fourier Feature Pairs for Statistical Independence Testing (NeurIPS 2024 · similarity 0.88)
- TRF: Learning Kernels with Tuned Random Features (AAAI 2022 · similarity 0.88)
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