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.Comment: Main Text: 25 pages Supplementary Material: 39 page