# On the Optimality of Misspecified Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2305.07241 · HTML: https://mlsanity.com/paper/2305.07241/

## 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 (most cited first, 16 of 16)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Spectrum Dependent Learning Curves in Kernel Regression and Wide Neural Networks](https://mlsanity.com/paper/2002.02561/) (2020)
- [Gaussian Processes and Kernel Methods: A Review on Connections and Equivalences](https://mlsanity.com/paper/1807.02582/) (2018)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Generalization Error Rates in Kernel Regression: The Crossover from the Noiseless to Noisy Regime](https://mlsanity.com/paper/2105.15004/) (2021)
- [Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passes](https://mlsanity.com/paper/1805.10074/) (2018)
- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spaces](https://mlsanity.com/paper/1801.06720/) (2018)
- [Optimal Rates for Regularized Conditional Mean Embedding Learning](https://mlsanity.com/paper/2208.01711/) (2022)
- [Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithms](https://mlsanity.com/paper/1801.07226/) (2018)
- [Analyzing the discrepancy principle for kernelized spectral filter learning algorithms](https://mlsanity.com/paper/2004.08436/) (2020)
- [Learning curves for Gaussian process regression with power-law priors and targets](https://mlsanity.com/paper/2110.12231/) (2021)
- [Kernel Truncated Randomized Ridge Regression: Optimal Rates and Low Noise Acceleration](https://mlsanity.com/paper/1905.10680/) (2019)
- [Optimal rates for the regularized learning algorithms under general source condition](https://mlsanity.com/paper/1611.01900/) (2016)
- [Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regression](https://mlsanity.com/paper/2211.10968/) (2022)
- [Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Condition](https://mlsanity.com/paper/2204.07856/) (2022)

## Built on by (most cited first, 20 of 20)

- [On the Asymptotic Learning Curves of Kernel Ridge Regression under Power-law Decay](https://mlsanity.com/paper/2309.13337/) (2023)
- [Optimal Rates for Vector-Valued Spectral Regularization Learning Algorithms](https://mlsanity.com/paper/2405.14778/) (2024)
- [Optimal Rate of Kernel Regression in Large Dimensions](https://mlsanity.com/paper/2309.04268/) (2023)
- [Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions](https://mlsanity.com/paper/2401.01270/) (2024)
- [Generalization Error Curves for Analytic Spectral Algorithms under Power-law Decay](https://mlsanity.com/paper/2401.01599/) (2024)
- [Smoothness Adaptive Hypothesis Transfer Learning](https://mlsanity.com/paper/2402.14966/) (2024)
- [Nested Expectations with Kernel Quadrature](https://mlsanity.com/paper/2502.18284/) (2025)
- [Optimal Kernel Quantile Learning with Random Features](https://mlsanity.com/paper/2408.13591/) (2024)
- [Transfer Learning for Kernel-based Regression](https://mlsanity.com/paper/2310.13966/) (2023)
- [Optimal Rates and Saturation for Noiseless Kernel Ridge Regression](https://mlsanity.com/paper/2402.15718/) (2024)
- [Regularized least squares learning with heavy-tailed noise is minimax optimal](https://mlsanity.com/paper/2505.14214/) (2025)
- [On the Pinsker bound of inner product kernel regression in large dimensions](https://mlsanity.com/paper/2409.00915/) (2024)
- [Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfer](https://mlsanity.com/paper/2501.10870/) (2025)
- [On the Saturation Effects of Spectral Algorithms in Large Dimensions](https://mlsanity.com/paper/2503.00504/) (2025)
- [Overlap-Adaptive Regularization for Conditional Average Treatment Effect Estimation](https://mlsanity.com/paper/2509.24962/) (2025)
- [Estimating Continuous Treatment Effects with Two-Stage Kernel Ridge Regression](https://mlsanity.com/paper/2604.13410/) (2026)
- [Towards a Statistical Understanding of Neural Networks: Beyond the Neural Tangent Kernel Theories](https://mlsanity.com/paper/2412.18756/) (2024)
- [Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression](https://mlsanity.com/paper/2602.18958/) (2026)
- [Large Dimensional Kernel Ridge Regression: Extending to Product Kernels](https://mlsanity.com/paper/2605.14524/) (2026)
- [Generalized nonparametric regression in reproducing kernel Hilbert spaces: Consistency and rates of convergence](https://mlsanity.com/paper/2606.22993/) (2026)

## 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.