Kernel regression methods for prediction of materials properties: Recent developments

Machine learning (ML) is increasingly used in chemical physics and materials science. One major area of thrust is machine learning of properties of molecules and solid materials from descriptors of chemical composition and structure. Recently, kernel regression methods of various flavors—such as kernel ridge regression, Gaussian process regression, and support vector machine—have attracted attention in such applications. Kernel methods allow benefiting simultaneously from the advantages of linear regressions and the superior expressive power of nonlinear kernels. In many applications, kernel methods are used in high-dimensional feature spaces, where sampling with training data is bound to be sparse and where effects specific to high-dimensional spaces significantly affect the performance of the method. We review recent applications of kernel-based methods for the prediction of properties of molecules and materials from descriptors of chemical composition and structure and related purposes. We discuss methodological aspects including choices of kernels appropriate for different applications, effects of dimensionality, and ways to balance expressive power and reliability of the model in high-dimensional feature spaces and with sparse data. We also discuss kernel regression-based hybrid ML approaches.