Understanding Kernel Ridge Regression: Common behaviors from simple functions to density functionals
This work provides theoretical insights into machine learning approximations for density functionals, which is incremental but useful for researchers in computational chemistry and materials science.
The paper investigates the error dependence on hyperparameters in kernel ridge regression by analyzing a simple one-variable function, revealing universal behaviors in extreme limits and applying these insights to machine learning models of density functionals.
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.