Fast Non-Parametric Tests of Relative Dependency and Similarity
  We introduce two novel non-parametric statistical hypothesis tests. The first
test, called the relative test of dependency, enables us to determine whether
one source variable is significantly more dependent on a first target variable
or a second. Dependence is measured via the Hilbert-Schmidt Independence
Criterion (HSIC). The second test, called the relative test of similarity, is
use to determine which of the two samples from arbitrary distributions is
significantly closer to a reference sample of interest and the relative measure
of similarity is based on the Maximum Mean Discrepancy (MMD). To construct
these tests, we have used as our test statistics the difference of HSIC
statistics and of MMD statistics, respectively. The resulting tests are
consistent and unbiased, and have favorable convergence properties. The
effectiveness of the relative dependency test is demonstrated on several
real-world problems: we identify languages groups from a multilingual parallel
corpus, and we show that tumor location is more dependent on gene expression
than chromosome imbalance. We also demonstrate the performance of the relative
test of similarity over a broad selection of model comparisons problems in deep
generative models.
