  Understanding the relationships between different properties of data, such as
whether a connectome or genome has information about disease status, is
becoming increasingly important in modern biological datasets. While existing
approaches can test whether two properties are related, they often require
unfeasibly large sample sizes in real data scenarios, and do not provide any
insight into how or why the procedure reached its decision. Our approach,
"Multiscale Graph Correlation" (MGC), is a dependence test that juxtaposes
previously disparate data science techniques, including k-nearest neighbors,
kernel methods (such as support vector machines), and multiscale analysis (such
as wavelets). Other methods typically require double or triple the number
samples to achieve the same statistical power as MGC in a benchmark suite
including high-dimensional and nonlinear relationships - spanning polynomial
(linear, quadratic, cubic), trigonometric (sinusoidal, circular, ellipsoidal,
spiral), geometric (square, diamond, W-shape), and other functions, with
dimensionality ranging from 1 to 1000. Moreover, MGC uniquely provides a simple
and elegant characterization of the potentially complex latent geometry
underlying the relationship, providing insight while maintaining computational
efficiency. In several real data applications, including brain imaging and
cancer genetics, MGC is the only method that can both detect the presence of a
dependency and provide specific guidance for the next experiment and/or
analysis to conduct.
