Kernel Methods for Quantum Chemistry

Kernel ridge regression (KRR) is one of the most popular methods of non-linear regression analysis in quantum chemistry. One of the main ingredients of KRR is the representation of the underlying physical system which mainly determines the performance of predicting quantum-mechanical properties based on KRR. Several such representations have been developed for both, solids and molecules; all of them with different advantages and limitations. These descriptors correspond to a similarity measure between two chemical compounds which is represented by the kernel. As recent approaches define the kernel directly from the underlying physical system, it is important to understand the properties of kernels and how these kernel properties can be used to improve the performance of machine learning models for quantum chemistry. After reviewing key representations of molecules, we provide an intuition on how the choice of the kernel affects the model. This is followed by a more practical guide of two complementary kernel methods, one for supervised and one for unsupervised learning, respectively. Finally, we present a way to gain an understanding about the model complexity by estimating the effective dimensionality induced by the data, the representation, and the kernel.