Data driven conditional optimal transport

Esteban G. Tabak, Giulio Trigila, Wenjun Zhao

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)3135-3155
Number of pages21
JournalMachine Learning
Issue number11-12
StatePublished - Dec 2021


  • Color transfer
  • Conditional average treatment effect
  • Image restoration
  • Optimal transport
  • Uncertainty quantification

ASJC Scopus subject areas

  • Software
  • Artificial Intelligence

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