Data driven conditional optimal transport

摘要

A data-driven procedure is developed to compute the optimal map between two conditional probabilities \(\rho (x|z_{1},\ldots ,z_{L})\) and \(\mu (y|z_{1},\ldots ,z_{L})\), known only through samples and depending on a set of covariates \(z_{l}\). 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.