# Adaptive Parameter Selection for Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2312.05885 · HTML: https://mlsanity.com/paper/2312.05885/

## 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 (most cited first, 12 of 12)

- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Early stopping and non-parametric regression: An optimal data-dependent stopping rule](https://mlsanity.com/paper/1306.3574/) (2013)
- [Optimal Rates For Regularization Of Statistical Inverse Learning Problems](https://mlsanity.com/paper/1604.04054/) (2016)
- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Analyzing the discrepancy principle for kernelized spectral filter learning algorithms](https://mlsanity.com/paper/2004.08436/) (2020)
- [Distributed Kernel Ridge Regression with Communications](https://mlsanity.com/paper/2003.12210/) (2020)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [Convergence rates of Kernel Conjugate Gradient for random design regression](https://mlsanity.com/paper/1607.02387/) (2016)
- [Analysis of regularized Nystr"om subsampling for regression functions of low smoothness](https://mlsanity.com/paper/1806.00826/) (2018)
- [Total stability of kernel methods](https://mlsanity.com/paper/1709.07625/) (2017)
- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)

## Built on by (most cited first, 3 of 3)

- [Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descents](https://mlsanity.com/paper/2603.03401/) (2026)
- [Integral Operator Approaches for Scattered Data Fitting on Spheres](https://mlsanity.com/paper/2401.15294/) (2024)
- [Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guarantees](https://mlsanity.com/paper/2608.25513/) (2026)

## 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.