From Mahalanobis to Bregman via Monge and Kantorovich
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DOI: 10.1007/s13571-018-0163-4
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- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Post-Print hal-03391975, HAL.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Sciences Po publications info:hdl:2441/64itsev5509, Sciences Po.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2014.
"Monge-Kantorovich Depth, Quantiles, Ranks, and Signs,"
Papers
1412.8434, arXiv.org, revised Sep 2015.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Sciences Po publications info:hdl:2441/64itsev5509, Sciences Po.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich depth, quantiles, ranks and signs," CeMMAP working papers CWP57/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich depth, quantiles, ranks and signs," CeMMAP working papers CWP04/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Sciences Po publications info:hdl:2441/3qnaslliat8, Sciences Po.
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- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks and Signs," Working Papers ECARES ECARES 2015-02, ULB -- Universite Libre de Bruxelles.
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"Monge-Kantorovich Depth, Quantiles, Ranks, and Signs,"
Papers
1412.8434, arXiv.org, revised Sep 2015.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Post-Print hal-03391975, HAL.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," SciencePo Working papers Main hal-03391975, HAL.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich depth, quantiles, ranks and signs," CeMMAP working papers CWP57/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich depth, quantiles, ranks and signs," CeMMAP working papers CWP04/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Sciences Po publications info:hdl:2441/3qnaslliat8, Sciences Po.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," SciencePo Working papers Main hal-03460056, HAL.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Working Papers hal-03460056, HAL.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2015. "Monge-Kantorovich Depth, Quantiles, Ranks and Signs," Working Papers ECARES ECARES 2015-02, ULB -- Universite Libre de Bruxelles.
- Victor Chernozhukov & Alfred Galichon & Marc Hallin & Marc Henry, 2017. "Monge-Kantorovich Depth, Quantiles, Ranks, and Signs," Sciences Po publications info:hdl:2441/64itsev5509, Sciences Po.
- Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2015.
"Vector quantile regression: an optimal transport approach,"
CeMMAP working papers
CWP58/15, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
- Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," SciencePo Working papers Main hal-03567920, HAL.
- Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," Post-Print hal-03567920, HAL.
- Guillaume Carlier & Victor Chernozhukov & Alfred Galichon, 2016. "Vector Quantile Regression: An Optimal Transport Approach," Sciences Po publications info:hdl:2441/4c5431jp6o8, Sciences Po.
- Eustasio Del Barrio & Juan Cuesta Albertos & Marc Hallin & Carlos Matran, 2018. "Smooth Cyclically Monotone Interpolation and Empirical Center-Outward Distribution Functions," Working Papers ECARES 2018-15, ULB -- Universite Libre de Bruxelles.
- Martin Burger, 2016. "Bregman Distances in Inverse Problems and Partial Differential Equations," Springer Optimization and Its Applications, in: Jean-Baptiste Hiriart-Urruty & Adam Korytowski & Helmut Maurer & Maciej Szymkat (ed.), Advances in Mathematical Modeling, Optimization and Optimal Control, pages 3-33, Springer.
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Keywords
Bregman divergence; Gradient of convex function; Mahalanobis distance; Measure transportation; McCann theorem; Monge-Kantorovich problem; Multivariate distribution function; Multivariate quantiles; Outlyingness;All these keywords.
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