Vector quantile regression and optimal transport, from theory to numerics

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

    Research output: Contribution to journalArticlepeer-review


    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 languageEnglish (US)
    Pages (from-to)35-62
    Number of pages28
    JournalEmpirical Economics
    Issue number1
    StatePublished - Jan 2022


    • 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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