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 Robert Müller; Kieron Burke

doi:10.1002/qua.24939

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 Robert Müller, Kieron Burke

Research output: Contribution to journal › Article › peer-review

88 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 language	English
Pages (from-to)	1115-1128
Number of pages	14
Journal	International Journal of Quantum Chemistry
Volume	115
Issue number	16
DOIs	https://doi.org/10.1002/qua.24939
Publication status	Published - 2015 Aug 1

Bibliographical note

Publisher Copyright:
© 2015 Wiley Periodicals, Inc.

Keywords

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

ASJC Scopus subject areas

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

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10.1002/qua.24939

Cite this

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AU - Müller, Klaus Robert

AU - Burke, Kieron

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KW - noise-free curve

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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