Metric learning for kernel ridge regression: assessment of molecular similarity

Supervised and unsupervised kernel-based algorithms widely used in the physical sciences depend upon the notion of similarity. Their reliance on pre-defined distance metrics-e.g. the Euclidean or Manhattan distance-are problematic especially when used in combination with high-dimensional feature vectors for which the similarity measure does not well-reflect the differences in the target property. Metric learning is an elegant approach to surmount this shortcoming and find a property-informed transformation of the feature space. We propose a new algorithm for metric learning specifically adapted for kernel ridge regression (KRR): metric learning for kernel ridge regression (MLKRR). It is based on the Metric Learning for Kernel Regression framework using the Nadaraya-Watson estimator, which we show to be inferior to the KRR estimator for typical physics-based machine learning tasks. The MLKRR algorithm allows for superior predictive performance on the benchmark regression task of atomisation energies of QM9 molecules, as well as generating more meaningful low-dimensional projections of the modified feature space.