(Psycho-)analysis of benchmark experiments: A formal framework for investigating the relationship between data sets and learning algorithms

It is common knowledge that the performance of different learning algorithms depends on certain characteristics of the data—such as dimensionality, linear separability or sample size. However, formally investigating this relationship in an objective and reproducible way is not trivial. A new formal framework for describing the relationship between data set characteristics and the performance of different learning algorithms is proposed. The framework combines the advantages of benchmark experiments with the formal description of data set characteristics by means of statistical and information-theoretic measures and with the recursive partitioning of Bradley–Terry models for comparing the algorithms’ performances. The formal aspects of each component are introduced and illustrated by means of an artificial example. Its real-world usage is demonstrated with an application example consisting of thirteen widely-used data sets and six common learning algorithms. The Appendix provides information on the implementation and the usage of the framework within the R language.