Nonparametric statistical analysis for multiple comparison of machine learning regression algorithms

In the paper we present some guidelines for the application of nonparametric statistical tests and post-hoc procedures devised to perform multiple comparisons of machine learning algorithms. We emphasize that it is necessary to distinguish between pairwise and multiple comparison tests. We show that the pairwise Wilcoxon test, when employed to multiple comparisons, will lead to overoptimistic conclusions. We carry out intensive normality examination employing ten different tests showing that the output of machine learning algorithms for regression problems does not satisfy normality requirements. We conduct experiments on nonparametric statistical tests and post-hoc procedures designed for multiple 1 ×N and N ×N comparisons with six different neural regression algorithms over 29 benchmark regression data sets. Our investigation proves the usefulness and strength of multiple comparison statistical procedures to analyse and select machine learning algorithms.