# Efficient Hyperparameter Tuning for Large Scale Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2201.06314 · HTML: https://mlsanity.com/paper/2201.06314/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 54 references that are in the map.
- First posted on arXiv 17 Jan 2022.

## Builds on (most cited first, 20 of 20)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [GPyTorch: Blackbox Matrix-Matrix Gaussian Process Inference with GPU Acceleration](https://mlsanity.com/paper/1809.11165/) (2018)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Gradient-based Hyperparameter Optimization through Reversible Learning](https://mlsanity.com/paper/1502.03492/) (2015)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Hyperparameter optimization with approximate gradient](https://mlsanity.com/paper/1602.02355/) (2016)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Kernel Operations on the GPU, with Autodiff, without Memory Overflows](https://mlsanity.com/paper/2004.11127/) (2020)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [Convergence of Sparse Variational Inference in Gaussian Processes Regression](https://mlsanity.com/paper/2008.00323/) (2020)
- [Fast Randomized Kernel Methods With Statistical Guarantees](https://mlsanity.com/paper/1411.0306/) (2014)
- [liquidSVM: A Fast and Versatile SVM package](https://mlsanity.com/paper/1702.06899/) (2017)
- [Hierarchically Compositional Kernels for Scalable Nonparametric Learning](https://mlsanity.com/paper/1608.00860/) (2016)

## Built on by (most cited first, 11 of 11)

- [Robustifying Generalizable Implicit Shape Networks with a Tunable Non-Parametric Model](https://mlsanity.com/paper/2311.12967/) (2023)
- [Stochastic Zeroth order Descent with Structured Directions](https://mlsanity.com/paper/2206.05124/) (2022)
- [Overparameterized random feature regression with nearly orthogonal data](https://mlsanity.com/paper/2211.06077/) (2022)
- [Hyperparameter Optimization for Randomized Algorithms: A Case Study on Random Features](https://mlsanity.com/paper/2407.00584/) (2024)
- [Explaining Preferences with Shapley Values](https://mlsanity.com/paper/2205.13662/) (2022)
- [A Theoretical Characterization of Optimal Data Augmentations in Self-Supervised Learning](https://mlsanity.com/paper/2411.01767/) (2024)
- [Regularization, early-stopping and dreaming: a Hopfield-like setup to address generalization and overfitting](https://mlsanity.com/paper/2308.01421/) (2023)
- [Learning Analysis of Kernel Ridgeless Regression with Asymmetric Kernel Learning](https://mlsanity.com/paper/2406.01435/) (2024)
- [Enhancing Kernel Flexibility via Learning Asymmetric Locally-Adaptive Kernels](https://mlsanity.com/paper/2310.05236/) (2023)
- [Top-Tuning: a study on transfer learning for an efficient alternative to fine tuning for image classification with fast kernel methods](https://mlsanity.com/paper/2209.07932/) (2022)
- [Comparing EPGP Surrogates and Finite Elements Under Degree-of-Freedom Parity](https://mlsanity.com/paper/2511.04518/) (2025)

## Abstract (arXiv)

Kernel methods provide a principled approach to nonparametric learning. While their basic implementations scale poorly to large problems, recent advances showed that approximate solvers can efficiently handle massive datasets. A shortcoming of these solutions is that hyperparameter tuning is not taken care of, and left for the user to perform. Hyperparameters are crucial in practice and the lack of automated tuning greatly hinders efficiency and usability. In this paper, we work to fill in this gap focusing on kernel ridge regression based on the Nystr"om approximation. After reviewing and contrasting a number of hyperparameter tuning strategies, we propose a complexity regularization criterion based on a data dependent penalty, and discuss its efficient optimization. Then, we proceed to a careful and extensive empirical evaluation highlighting strengths and weaknesses of the different tuning strategies. Our analysis shows the benefit of the proposed approach, that we hence incorporate in a library for large scale kernel methods to derive adaptively tuned solutions.