# Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals

arXiv: https://arxiv.org/abs/1501.03854 · HTML: https://mlsanity.com/paper/1501.03854/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jan 2015.

## Built on by (most cited first, 4 of 4)

- [Bayesian Optimization of Catalysis With In-Context Learning](https://mlsanity.com/paper/2304.05341/) (2023)
- [Multi-Fidelity Machine Learning for Excited State Energies of Molecules](https://mlsanity.com/paper/2305.11292/) (2023)
- [Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension](https://mlsanity.com/paper/2311.10790/) (2023)
- [The loss of the property of locality of the kernel in high-dimensional Gaussian process regression on the example of the fitting of molecular potential energy surfaces](https://mlsanity.com/paper/2211.11170/) (2022)

## Abstract (arXiv)

Accurate approximations to density functionals have recently been obtained via machine learning (ML). By applying ML to a simple function of one variable without any random sampling, we extract the qualitative dependence of errors on hyperparameters. We find universal features of the behavior in extreme limits, including both very small and very large length scales, and the noise-free limit. We show how such features arise in ML models of density functionals.