Editing Cross-validation (statistics) (section)

===k*l-fold cross-validation===

This is a truly nested variant which contains an outer loop of ''k'' sets and an inner loop of ''l'' sets. The total data set is split into ''k'' sets. One by one, a set is selected as the (outer) test set and the ''k''&nbsp;-&nbsp;1 other sets are combined into the corresponding outer training set. This is repeated for each of the ''k'' sets. Each outer training set is further sub-divided into ''l'' sets.  One by one, a set is selected as inner test (validation) set and the ''l''&nbsp;-&nbsp;1 other sets are combined into the corresponding inner training set. This is repeated for each of the ''l'' sets. The inner training sets are used to fit model parameters, while the outer test set is used as a validation set to provide an unbiased evaluation of the model fit. Typically, this is repeated for many different hyperparameters (or even different model types) and the validation set is used to determine the best hyperparameter set (and model type) for this inner training set. After this, a new model is fit on the entire outer training set, using the best set of hyperparameters from the inner cross-validation. The performance of this model is then evaluated using the outer test set.