  In this paper, a robust non-parametric measure of statistical dependence, or
correlation, between two random variables is presented. The proposed
coefficient is a permutation-like statistic that quantifies how much the
observed sample S_n : {(X_i , Y_i), i = 1 . . . n} is discriminable from the
permutated sample ^S_nn : {(X_i , Y_j), i, j = 1 . . . n}, where the two
variables are independent. The extent of discriminability is determined using
the predictions for the, interchangeable, leave-out sample from training an
aggregate of decision trees to discriminate between the two samples without
materializing the permutated sample. The proposed coefficient is
computationally efficient, interpretable, invariant to monotonic
transformations, and has a well-approximated distribution under independence.
Empirical results show the proposed method to have a high power for detecting
complex relationships from noisy data.
