Enumerating the k-fold configurations in multi-class classification problems

K-fold cross-validation is a widely used tool for assessing classifier performance. The reproducibility crisis faced by artificial intelligence partly results from the irreproducibility of reported k-fold cross-validation-based performance scores. Recently, we introduced numerical techniques to test the consistency of claimed performance scores and experimental setups. In a crucial use case, the method relies on the combinatorial enumeration of all k-fold configurations, for which we proposed an algorithm in the binary classification case.