Understanding kernel ridge regression: Common behaviors from simple functions to density functionals

Kevin Vu, John C. Snyder, Li Li, Matthias Rupp, Brandon F. Chen, Tarek Khelif, Klaus Muller, Kieron Burke

Research output: Contribution to journalArticle

35 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)1115-1128
Number of pages14
JournalInternational Journal of Quantum Chemistry
Volume115
Issue number16
DOIs
Publication statusPublished - 2015 Aug 1

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machine learning
functionals
Learning systems
ridges
regression analysis
random sampling
Sampling
approximation

Keywords

  • density functional theory
  • extreme behaviors
  • hyperparameters optimization
  • machine learning
  • noise-free curve

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Atomic and Molecular Physics, and Optics
  • Physical and Theoretical Chemistry

Cite this

Understanding kernel ridge regression : Common behaviors from simple functions to density functionals. / Vu, Kevin; Snyder, John C.; Li, Li; Rupp, Matthias; Chen, Brandon F.; Khelif, Tarek; Muller, Klaus; Burke, Kieron.

In: International Journal of Quantum Chemistry, Vol. 115, No. 16, 01.08.2015, p. 1115-1128.

Research output: Contribution to journalArticle

Vu, K, Snyder, JC, Li, L, Rupp, M, Chen, BF, Khelif, T, Muller, K & Burke, K 2015, 'Understanding kernel ridge regression: Common behaviors from simple functions to density functionals', International Journal of Quantum Chemistry, vol. 115, no. 16, pp. 1115-1128. https://doi.org/10.1002/qua.24939
Vu, Kevin ; Snyder, John C. ; Li, Li ; Rupp, Matthias ; Chen, Brandon F. ; Khelif, Tarek ; Muller, Klaus ; Burke, Kieron. / Understanding kernel ridge regression : Common behaviors from simple functions to density functionals. In: International Journal of Quantum Chemistry. 2015 ; Vol. 115, No. 16. pp. 1115-1128.
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