Vector quantile regression and optimal transport, from theory to numerics

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

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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. (2016, 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.

Date: 2021-02
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Published in Empirical Economics (2020)

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http://arxiv.org/pdf/2102.12809 Latest version (application/pdf)

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Journal Article: Vector quantile regression and optimal transport, from theory to numerics (2022)
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