Flexible non-parametric tests of sample exchangeability and feature independence

In scientific studies involving analyses of multivariate data, two questions often arise for the researcher. First, is the sample exchangeable, meaning that the joint distribution of the sample is invariant to the ordering of the units? Second, are the features independent of one another, or can the features be grouped so that the groups are mutually independent? We propose a non-parametric approach that addresses these two questions. Our approach is conceptually simple, yet fast and flexible. It controls the Type I error across realistic scenarios, and handles data of arbitrary dimensions by leveraging large-sample asymptotics. In the exchangeability detection setting, through extensive simulations and a comparison against unsupervised tests of stratification based on random matrix theory, we find that our approach compares favorably in various scenarios of interest. We apply our method to problems in population and statistical genetics, including stratification detection and linkage disequilibrium splitting. We also consider other application domains, applying our approach to post-clustering single-cell chromatin accessibility data and World Values Survey data, where we show how users can partition features into independent groups, which helps generate new scientific hypotheses about the features.