Data driven conditional optimal transport

Esteban G. Tabak; Giulio Trigila; Wenjun Zhao

doi:10.1007/s10994-021-06060-0

Data driven conditional optimal transport

Esteban G. Tabak, Giulio Trigila, Wenjun Zhao

Mathematics

Research output: Contribution to journal › Article › peer-review

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) , 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.

Original language	English (US)
Pages (from-to)	3135-3155
Number of pages	21
Journal	Machine Learning
Volume	110
Issue number	11-12
DOIs	https://doi.org/10.1007/s10994-021-06060-0
State	Published - Dec 2021

Keywords

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

ASJC Scopus subject areas

Software
Artificial Intelligence

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10.1007/s10994-021-06060-0

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title = "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.",

keywords = "Color transfer, Conditional average treatment effect, Image restoration, Optimal transport, Uncertainty quantification",

author = "Tabak, {Esteban G.} and Giulio Trigila and Wenjun Zhao",

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AU - Tabak, Esteban G.

AU - Trigila, Giulio

AU - Zhao, Wenjun

N1 - Funding Information: The work of E. G. Tabak and W. Zhao was partially supported by NSF Grant DMS-1715753 and ONR Grant N00014-15-1-2355. Publisher Copyright: © 2021, The Author(s), under exclusive licence to Springer Science+Business Media LLC, part of Springer Nature.

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N2 - 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.

AB - 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.

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KW - Conditional average treatment effect

KW - Image restoration

KW - Optimal transport

KW - Uncertainty quantification

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Data driven conditional optimal transport

Abstract

Keywords

ASJC Scopus subject areas

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