mlsanityData to 14 Oct 2026

On the Optimality of Misspecified Kernel Ridge Regression

arXiv 2305.07241 ↗First posted 12 May 2023cs.LG math.ST stat.THcited by 20

Not on the map. Why?

Abstract (arXiv)

In the misspecified kernel ridge regression problem, researchers usually assume the underground true function fρ* ∈ [H]s, a less-smooth interpolation space of a reproducing kernel Hilbert space (RKHS) H for some s∈ (0,1). The existing minimax optimal results require |fρ*|_L∞<∞ which implicitly requires s > α0 where α0∈ (0,1) is the embedding index, a constant depending on H. Whether the KRR is optimal for all s∈ (0,1) is an outstanding problem lasting for years. In this paper, we show that KRR is minimax optimal for any s∈ (0,1) when the H is a Sobolev RKHS.

Key facts. Cited by 20 papers in the map (data through 14 Oct 2026). Builds on 16 of its 39 references that are in the map. First posted on arXiv 12 May 2023.

Builds on

16 of 39 references.

References · 16

  1. 2018Neural Tangent Kernel: Convergence and Generalization in Neural Networkscited by 2,621
  2. 2020Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networkscited by 200
  3. 2018Gaussian Processes and Kernel Methods: A Review on Connections and Equivalencescited by 192
  4. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 114
  5. 2021Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regimecited by 96
  6. 2018Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passescited by 69
  7. 2016Optimal Rates For Regularization Of Statistical Inverse Learning Problemscited by 68
  8. 2018Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spacescited by 59
  9. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  10. 2018Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithmscited by 22
  11. 2020Analyzing the discrepancy principle for kernelized spectral filter learning algorithmscited by 15
  12. 2021Learning curves for Gaussian process regression with power-law priors and targetscited by 15
4 more
  1. 2019Kernel Truncated Randomized Ridge Regression: Optimal Rates and Low Noise Accelerationcited by 12
  2. 2016Optimal rates for the regularized learning algorithms under general source conditioncited by 11
  3. 2022Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regressioncited by 8
  4. 2022Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Conditioncited by 2

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 8; 2025: 5; 2026: 4.

20 papers.

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  1. 2023On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decaycited by 19
  2. 2024Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithmscited by 12
  3. 2023Optimal Rate of Kernel Regression in Large Dimensionscited by 11
  4. 2024Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensionscited by 11
  5. 2024Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decaycited by 11
  6. 2024Smoothness Adaptive Hypothesis Transfer Learningcited by 8
  7. 2025Nested Expectations with Kernel Quadraturecited by 5
  8. 2024Optimal Kernel Quantile Learning with Random Featurescited by 4
  9. 2023Transfer Learning for Kernel-based Regressioncited by 3
  10. 2024Optimal Rates and Saturation for Noiseless Kernel Ridge Regressioncited by 3
  11. 2025Regularized least squares learning with heavy-tailed noise is minimax optimalcited by 3
  12. 2024On the Pinsker bound of inner product kernel regression in large dimensionscited by 2
8 more
  1. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  2. 2025On the Saturation Effects of Spectral Algorithms in Large Dimensionscited by 2
  3. 2025Overlap-Adaptive Regularization for Conditional Average Treatment Effect Estimationcited by 1
  4. 2026Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regressioncited by 1
  5. 2024Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theoriescited by 0
  6. 2026Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regressioncited by 0
  7. 2026Large Dimensional Kernel Ridge Regression: Extending to Product Kernelscited by 0
  8. 2026Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergencecited by 0