Vector quantile regression and optimal transport, from theory to numerics
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181_2020_Article_1919.pdf
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1.24 MB
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Checksum (MD5)
d538497b691e5819f73708523861c926
Author(s)
Carlier, Guillaume
Chernozhukov, Victor
De Bie, Gwendoline
Galichon, Alfred
Date Issued
August 12, 2020
Publisher
Springer Berlin Heidelberg
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Economics
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Creative Commons Attribution
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DOI of Published Version
https://doi.org/10.1007/s00181-020-01919-y
