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

Accurate approximations to density functionals have recently been obtained\nvia machine learning (ML). By applying ML to a simple function of one variable\nwithout any random sampling, we extract the qualitative dependence of errors on\nhyperparameters. We find universal features of the behavior in extreme limits,\nincluding both very small and very large length scales, and the noise-free\nlimit. We show how such features arise in ML models of density functionals.\n