The optimal descriptor complexity with respect to its predictability is determined by using a leave-one-materialout cross-validation strategy (see details in SI, Figs. ). This is done to prevent overfitting to the data set, as the expressions generated by SISSO are flexible and could easily fit the rather small number of materials used in this work nearly exactly but with the result of a lower prediction quality. The optimal complexity is considered the one which minimizes the averaged root-mean-squared error evaluated on left-out (predicted) materials (CV-RMSE).