Data driven conditional optimal transport

Abstract

A data-driven procedure is developed to compute the optimal map between two conditional probabilities ρ(x| z1, … , zL) and μ(y| z1, … , zL) , known only through samples and depending on a set of covariates zl. The procedure is tested on synthetic data from the ACIC Data Analysis Challenge 2017 and it is applied to non-uniform lightness transfer between images. Exactly solvable examples and simulations are performed to highlight the differences with ordinary optimal transport.