The nested Sinkhorn divergence to learn the nested distance

Abstract The nested distance builds on the Wasserstein to quantify difference of stochastic processes, including also evolution information modelled by filtrations. Sinkhorn divergence is a relaxation distance, which can be computed considerably faster. For this reason we employ and take advantage related (fixed point) iteration algorithm. Furthermore, investigate transition entropy throughout stages process provide an entropy-regularized formulation, characterization its dual. Numerical experiments affirm computational supremacy.