  Identifying statistical dependence between the features and the label is a
fundamental problem in supervised learning. This paper presents a framework for
estimating dependence between numerical features and a categorical label using
generalized Gini distance, an energy distance in reproducing kernel Hilbert
spaces (RKHS). Two Gini distance based dependence measures are explored: Gini
distance covariance and Gini distance correlation. Unlike Pearson covariance
and correlation, which do not characterize independence, the above Gini
distance based measures define dependence as well as independence of random
variables. The test statistics are simple to calculate and do not require
probability density estimation. Uniform convergence bounds and asymptotic
bounds are derived for the test statistics. Comparisons with distance
covariance statistics are provided. It is shown that Gini distance statistics
converge faster than distance covariance statistics in the uniform convergence
bounds, hence tighter upper bounds on both Type I and Type II errors. Moreover,
the probability of Gini distance covariance statistic under-performing the
distance covariance statistic in Type II error decreases to 0 exponentially
with the increase of the sample size. Extensive experimental results are
presented to demonstrate the performance of the proposed method.
