Correction to: Vector Quantile Regression and Optimal Transport, from Theory to Numerics

Guillaume Carlier (1, 2, 3) , Victor Chernozhukov (4) , Gwendoline de Bie (5) , Alfred Galichon (6, 7)

1 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision
2 Université Paris Dauphine-PSL
3 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
4 MIT - Massachusetts Institute of Technology
5 DMA - Département de Mathématiques et Applications - ENS Paris
6 NYU - New York University [New York]
7 ECON - Département d'économie (Sciences Po)

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.

Mots clés: Vector quantile regression; Optimal transport with mean independence constraints; Latent factors; Entropic regularization

Domaines: Economies et finances

Guillaume Carlier, Victor Chernozhukov, Gwendoline de Bie, Alfred Galichon. Correction to: Vector Quantile Regression and Optimal Transport, from Theory to Numerics. Empirical Economics, 2022, 62 (1), pp.63-63. ⟨10.1007/s00181-020-01933-0⟩. ⟨hal-03896159⟩