This question relates to model selection and validation. This post laid out three strategies on how to deal with very small n. In conclusion (option 3), one might resign using a global test set, but use every instance for training. The use of cross validation still allows to get average performance indicators on the validation folds (for the sake of this question: regardless if single or nested). Is there any (scientifically) safe rule on when one might abstain from having a global test set?

The question is based on these two discussions:

No need of global testing set with small n

Possibilities to deal with small n, w/o global test set


1 Answer 1


I think if you look carefully you will find your answer in the posts that you have linked. The case of global test set is the best case scenario often referred to as three-way-split which is recommended for large datasets. However, for smaller datasets, this isn't feasible and you can revert to the k-fold cross-validation. But taking care about following issues:

  1. Use different k-fold cross-validation for model selection, i.e., optimizing the parameters and determining the generalization capability of the model. First optimize model parameters with one round of cross-validation and second determine their generalization capability.

  2. Since number of samples are small, try repeating k-fold cross-validation with different random splits which helps eliminate variance.

This two methods above have been scientifically accepted across literature, especially repeated cross validation: The relevant literature is Beleites, C. & Salzer, R.: Assessing and improving the stability of chemometric models in small sample size situations, Anal Bioanal Chem, 390, 1261-1271 (2008). http://link.springer.com/article/10.1007%2Fs00216-007-1818-6


However, these procedures as you have hinted may not produce best results and there are considerable issues when reporting k-fold CV results as detailed here:Cross-validation misuse (reporting performance for the best hyperparameter value)


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