Data driven conditional optimal transport

A data-driven procedure is developed to compute the optimal map between two conditional probabilities $$\rho (x|z_{1},\ldots ,z_{L})$$ and $$\mu (y|z_{1},\ldots , known only through samples depending on a set of covariates $$z_{l}$$ . The tested synthetic data from ACIC Data Analysis Challenge 2017 it applied non-uniform lightness transfer images. Exactly solvable examples simulations are performed highlight differences with ordinary transport.