Exploring and measuring non-linear correlations: Copulas, Lightspeed Transportation and Clustering

We propose a methodology to explore and measure the pairwise correlations that exist between variables in a dataset. The methodology leverages copulas for encoding dependence between two variables, state-of-the-art optimal transport for providing a relevant geometry to the copulas, and clustering for summarizing the main dependence patterns found between the variables. Some of the clusters centers can be used to parameterize a novel dependence coefficient which can target or forget specific dependence patterns. Finally, we illustrate the methodology with financial time series (credit default swaps, stocks, foreign exchange rates). Code and numerical experiments are available online at https://www.datagrapple.com/Tech for reproducible research.