Vector quantile regression and optimal transport, from theory to numerics

Guillaume Carlier; Victor Chernozhukov; Gwendoline De Bie; Alfred Galichon

doi:10.1007/s00181-020-01919-y

Vector quantile regression and optimal transport, from theory to numerics

Guillaume Carlier, Victor Chernozhukov, Gwendoline De Bie, Alfred Galichon

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

Abstract

In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate extension due to Carlier et al. (Ann Statist 44(3):1165–92, 2016,; J Multivariate Anal 161:96–102, 2017) which relates vector quantile regression to an optimal transport problem with mean independence constraints. We introduce an entropic regularization of this problem, implement a gradient descent numerical method and illustrate its feasibility on univariate and bivariate examples.

Original language	English (US)
Pages (from-to)	35-62
Number of pages	28
Journal	Empirical Economics
Volume	62
Issue number	1
DOIs	https://doi.org/10.1007/s00181-020-01919-y
State	Published - Jan 2022

Keywords

Entropic regularization
Latent factors
Optimal transport with mean independence constraints
Vector quantile regression

ASJC Scopus subject areas

Statistics and Probability
Mathematics (miscellaneous)
Social Sciences (miscellaneous)
Economics and Econometrics

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10.1007/s00181-020-01919-y

Cite this

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abstract = "In this paper, we first revisit the Koenker and Bassett variational approach to (univariate) quantile regression, emphasizing its link with latent factor representations and correlation maximization problems. We then review the multivariate extension due to Carlier et al. (Ann Statist 44(3):1165–92, 2016,; J Multivariate Anal 161:96–102, 2017) which relates vector quantile regression to an optimal transport problem with mean independence constraints. We introduce an entropic regularization of this problem, implement a gradient descent numerical method and illustrate its feasibility on univariate and bivariate examples.",

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author = "Guillaume Carlier and Victor Chernozhukov and {De Bie}, Gwendoline and Alfred Galichon",

note = "Funding Information: Funding from R{\'e}gion Ile-de-France grant is acknowledged. Funding from NSF Grant DMS-1716489 is acknowledged. Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

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AU - Carlier, Guillaume

AU - Chernozhukov, Victor

AU - De Bie, Gwendoline

AU - Galichon, Alfred

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Vector quantile regression and optimal transport, from theory to numerics

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Keywords

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