Vector quantile regression and optimal transport, from theory to numerics

@article{Carlier2020VectorQR,
  title={Vector quantile regression and optimal transport, from theory to numerics},
  author={Guillaume Carlier and Victor Chernozhukov and Gwendoline De Bie and Alfred Galichon},
  journal={Empirical Economics},
  year={2020},
  volume={62},
  pages={35-62}
}
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… 

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Regression Quantiles