Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals
Computational Physics
2015-01-29 v2 Machine Learning
Machine Learning
Abstract
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.
Cite
@article{arxiv.1501.03854,
title = {Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals},
author = {Kevin Vu and John Snyder and Li Li and Matthias Rupp and Brandon F. Chen and Tarek Khelif and Klaus-Robert Müller and Kieron Burke},
journal= {arXiv preprint arXiv:1501.03854},
year = {2015}
}
Comments
15 pages, 20 figures