Fig. 6: Common validation approaches.

a Two-way hold-out method (a single split of the whole dataset into training and testing sets). b Three-way hold-out method (a single split of the whole dataset into training, validation, and testing sets). c k-fold outer cross-validation (CV; on the whole dataset). d k-fold inner CV (a single split of the whole dataset into training and testing sets, followed by CV on the training set). e n × k nested CV with n-fold outer CV loops each containing k-fold inner CV. For illustration purposes, an 80/20 split was showcased in methods (a) and (d) for the training/testing split; a 60/20/20 split was showcased in method (b) for the training/validation/testing split; and both n and k were set as 5 for CV approaches. Note that methods (a) and (c) are merely used for model evaluation, while the remaining methods can be adopted for both model selection and model evaluation.