We introduce a new algorithm, called the swapping algorithm, to approximate numerically the minimal and maximal expected inner product of two random vectors with given marginal distributions. As a direct application, the algorithm computes an approximation of the L2-Wasserstein distance between...

We study properties of the Rearrangement Algorithm (RA) in the context of inferring dependence among variables given their marginal distributions and the distribution of the sum. We show that the RA yields solutions that are “close to each other” and exhibit almost maximum entropy. The...