Chemical machine learning with kernels: The impact of loss functions

Machine learning promises to accelerate materials discovery by allowing computational efficient property predictions from a small number of reference calculations. As a result, the literature has spent a considerable effort in designing representations that capture basic physical properties. Our work focuses on the less-studied learning formulations in this context in order to exploit inner structures in the prediction errors. In particular, we propose to directly optimize basic loss functions of the prediction error metrics typically used in the literature, such as the mean absolute error or the worst case error. In some instances, a proper choice of the loss function can directly reduce reasonably the prediction performance in the desired metric, albeit at the cost of additional computations during training. To support this claim, we describe the statistical learning theoretic foundations, and provide supporting numerical evidence with the prediction of atomization energies for a database of small organic molecules.