Performance is not enough: a story of the Rashomon's quartet

Predictive modelling is often reduced to finding the best model that optimizes a selected performance measure. But what if the second-best model describes the data equally well but in a completely different way? What about the third? Is it possible that the most effective models learn completely different relationships in the data? Inspired by Anscombe's quartet, this paper introduces Rashomon's quartet, a synthetic dataset for which four models from different classes have practically identical predictive performance. However, their visualization reveals drastically distinct ways of understanding the correlation structure in data. The introduced simple illustrative example aims to further facilitate visualization as a mandatory tool to compare predictive models beyond their performance. We need to develop insightful techniques for the explanatory analysis of model sets.