Vector quantile regression and optimal transport, from theory to numerics

Vector quantile regression and optimal transport, from theory to numerics

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. (Ann Statist 44(3)...

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Main Authors: Carlier, Guillaume (Author), Chernozhukov, Victor (Author), De Bie, Gwendoline (Author), Galichon, Alfred (Author)
Format: Article
Language:English
Published: Springer Berlin Heidelberg, 2021-09-20T17:28:49Z.
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Online Access:Get fulltext
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100 1 0 |a Carlier, Guillaume  |e author 
700 1 0 |a Chernozhukov, Victor  |e author 
700 1 0 |a De Bie, Gwendoline  |e author 
700 1 0 |a Galichon, Alfred  |e author 
245 0 0 |a Vector quantile regression and optimal transport, from theory to numerics 
260 |b Springer Berlin Heidelberg,   |c 2021-09-20T17:28:49Z. 
856 |z Get fulltext  |u https://hdl.handle.net/1721.1/131584 
520 |a 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. (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. 
546 |a en 
655 7 |a Article 

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