Efficient hyperparameter tuning for kernel ridge regression with Bayesian optimization

Machine learning methods usually depend on internal parameters-so called hyperparameters-that need to be optimized for best performance. Such optimization poses a burden on machine learning practitioners, requiring expert knowledge, intuition or computationally demanding brute-force parameter searches. We here assess three different hyperparameter selection methods: Grid search, random search and an efficient automated optimization technique based on Bayesian optimization (BO). We apply these methods to a machine learning problem based on kernel ridge regression in computational chemistry. Two different descriptors are employed to represent the atomic structure of organic molecules, one of which introduces its own set of hyperparameters to the method. We identify optimal hyperparameter configurations and infer entire prediction error landscapes in hyperparameter space that serve as visual guides for the hyperparameter performance. We further demonstrate that for an increasing number of hyperparameters, BO and random search become significantly more efficient in computational time than an exhaustive grid search, while delivering an equivalent or even better accuracy.