Data Driven Conditional Optimal Transport

2019/10/24 by Esteban G. Tabak, Tabak, Esteban G., Giulio Trigila +3 · 4 citations
Biochemistry, Genetics and Molecular Biology · Chemistry · Computer Science · #Cell Image Analysis Techniques #FOS: Mathematics #Image and Signal Denoising Methods #Optimization and Control (math.OC) #Spectroscopy and Chemometric Analyses

paper · pdf · doi:10.48550/arxiv.1910.11422

openalex publication_date 2019/10/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A data driven procedure is developed to compute the optimal map between two conditional probabilities ρ(x|z₁,...,z_L) and μ(y|z₁,...,z_L) depending on a set of covariates z_i. 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.

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