Vector quantile regression and optimal transport, from theory to numerics
General Economics
2021-02-26 v1 Economics
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.
Keywords
Cite
@article{arxiv.2102.12809,
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= {arXiv preprint arXiv:2102.12809},
year = {2021}
}
Comments
35 pages, 19 figures, 4 tables. arXiv admin note: text overlap with arXiv:1610.06833