Stochastic optimal transport in Banach Spaces for regularized estimation of multivariate quantiles

arXiv:2302.00982v2 Announce Type: replace-cross
Abstract: We introduce a new stochastic algorithm for solving entropic optimal transport (EOT) between two absolutely continuous probability measures $\mu$ and $\nu$. Our work is motivated by the specific setting of Monge-Kantorovich quantiles where the source measure $\mu$ is either the uniform distribution on the unit hypercube or the spherical uniform distribution. Using the knowledge of the source measure, we propose to parametrize a Kantorovich dual potential by its Fourier coefficients. In this way, each iteration …

abstract algorithm arxiv continuous distribution math.pr multivariate probability spaces stat.ml stochastic transport type uniform work