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Understanding kernel ridge regression: Common behaviors from simple functions to density functionals
Author(s) -
Vu Kevin,
Snyder John C.,
Li Li,
Rupp Matthias,
Chen Brandon F.,
Khelif Tarek,
Müller KlausRobert,
Burke Kieron
Publication year - 2015
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.24939
Subject(s) - limit (mathematics) , hyperparameter , simple (philosophy) , statistical physics , kernel (algebra) , regression , mathematics , function (biology) , ridge , noise (video) , sampling (signal processing) , computer science , algorithm , artificial intelligence , statistics , physics , mathematical analysis , geology , combinatorics , paleontology , philosophy , epistemology , filter (signal processing) , evolutionary biology , computer vision , biology , image (mathematics)
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. © 2015 Wiley Periodicals, Inc.