mlsanityData to 14 Oct 2026

Adaptive Parameter Selection for Kernel Ridge Regression

arXiv 2312.05885 ↗First posted 10 Dec 2023cs.LG math.ST stat.THcited by 3

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Abstract (arXiv)

This paper focuses on parameter selection issues of kernel ridge regression (KRR). Due to special spectral properties of KRR, we find that delicate subdivision of the parameter interval shrinks the difference between two successive KRR estimates. Based on this observation, we develop an early-stopping type parameter selection strategy for KRR according to the so-called Lepskii-type principle. Theoretical verifications are presented in the framework of learning theory to show that KRR equipped with the proposed parameter selection strategy succeeds in achieving optimal learning rates and adapts to different norms, providing a new record of parameter selection for kernel methods.

Key facts. Cited by 3 papers in the map (data through 14 Oct 2026). Builds on 12 of its 31 references that are in the map. First posted on arXiv 10 Dec 2023.

Builds on

12 of 31 references.

References · 12

  1. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 114
  2. 2013Early stopping and non-parametric regression: An optimal data-dependent stopping rulecited by 89
  3. 2016Optimal Rates For Regularization Of Statistical Inverse Learning Problemscited by 68
  4. 2013Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Ratescited by 65
  5. 2016Distributed learning with regularized least squarescited by 42
  6. 2020Analyzing the discrepancy principle for kernelized spectral filter learning algorithmscited by 15
  7. 2020Distributed Kernel Ridge Regression with Communicationscited by 14
  8. 2015Optimal Learning Rates for Localized SVMscited by 13
  9. 2016Convergence rates of Kernel Conjugate Gradient for random design regressioncited by 8
  10. 2018Analysis of regularized Nystr"om subsampling for regression functions of low smoothnesscited by 7
  11. 2017Total stability of kernel methodscited by 5
  12. 2021Total Stability of SVMs and Localized SVMscited by 4

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2024: 1; 2025: 0; 2026: 2.

3 papers.

  1. 2026Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descentscited by 1
  2. 2024Integral Operator Approaches for Scattered Data Fitting on Spherescited by 0
  3. 2026Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guaranteescited by 0