Research map / Learning theory and algorithms / Kernels and regression theory
Optimal Rates of Sketched-regularized Algorithms for Least-Squares Regression over Hilbert Spaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a randomized sketch with dimension meeting the stated lower bound | Sketched-regularized algorithms · Least-squares regression over Hilbert spaces | ‖L⁻ᵃ(fλᶻ−fH)‖ρ error rate: n^{-(ζ-a)} (1 + (γ log n)^{2-a}); n^{-(ζ-a)/(2ζ+γ)} | Helped |
| Use Nyström subsampling with the stated sample dimension | Nyström regularized algorithms · Least-squares regression over Hilbert spaces; 2ζ+γ>1 | ‖L⁻ᵃ(fλᶻ−fH)‖ρ error rate: n^{- (ζ-a) / (2ζ+γ)} | Helped |
| Allow target regularity ζ≥1 in the analysis | Sketched- and Nyström-regularized algorithms · Least-squares regression over Hilbert spaces | Convergence rate | Helped |
| Restrict the estimator to a projected subspace with sufficiently small projection error | Projected-regularized algorithms · Least-squares regression over Hilbert spaces | ‖L⁻ᵃ(fλᶻ−fH)‖ρ error rate | No clear effect |
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