Measuring the complexity of regression problems

Many works have attempted to characterize the complexity of classification problems by measures extracted from their learning datasets. These indexes provide indicatives of the inherent difficulty in solving a given classification problem. Although regression problems are equally frequent, there is a lack of studies in Machine Learning dedicated to understanding their complexity. This paper proposes some measures aimed to characterize the complexity of regression problems. They are experimentally evaluated on a set of synthetic datasets with different complexities. The results show that various measures and their combinations are able to distinguish simple linear problems from more complex variants.