mlsanityData to 7 Oct 2026

On the Saturation Effect of Kernel Ridge Regression

arXiv 2405.09362 ↗First posted 15 May 2024stat.ML cs.LGcited by 12

Not on the map. Why?

Abstract (arXiv)

The saturation effect refers to the phenomenon that the kernel ridge regression (KRR) fails to achieve the information theoretical lower bound when the smoothness of the underground truth function exceeds certain level. The saturation effect has been widely observed in practices and a saturation lower bound of KRR has been conjectured for decades. In this paper, we provide a proof of this long-standing conjecture.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Builds on 5 of its 35 references that are in the map. First posted on arXiv 15 May 2024.

Builds on

5 of 35 references.

References · 5

  1. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  2. 2016Optimal Rates For Regularization Of Statistical Inverse Learning Problemscited by 68
  3. 2018Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spacescited by 59
  4. 2018Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithmscited by 22
  5. 2016Optimal rates for the regularized learning algorithms under general source conditioncited by 11

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 6; 2025: 4; 2026: 2.

12 papers.

  1. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
  2. 2024The Optimality of (Accelerated) SGD for High-Dimensional Quadratic Optimizationcited by 6
  3. 2024A Comprehensive Analysis on the Learning Curve in Kernel Ridge Regressioncited by 6
  4. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3
  5. 2025Learning Curves of Stochastic Gradient Descent in Kernel Regressioncited by 3
  6. 2024Improving Adaptivity via Over-Parameterization in Sequence Modelscited by 2
  7. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  8. 2025On the Saturation Effects of Spectral Algorithms in Large Dimensionscited by 2
  9. 2024A Kernel Perspective on Distillation-based Collaborative Learningcited by 1
  10. 2024Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theoriescited by 0
  11. 2026Large Dimensional Kernel Ridge Regression: Extending to Product Kernelscited by 0
  12. 2026Functional linear regression from sparse to dense designs: a pooling-ridge method and minimax optimalitycited by 0