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Quantile regression (QR) is a powerful tool for estimating one or more conditional quantiles of a target variable $\mathrm{Y}$ given explanatory features $\boldsymbol{\mathrm{X}}$.
Conjugate duality and optimization
R Tyrrell Rockafellar · 1974
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Regression Quantiles
Roger Koenker and Gilbert Bassett · 1978
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Polar factorization and monotone rearrangement of vector-valued functions
Yann Brenier · 1991
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Existence and uniqueness of monotone measure-preserving maps
Robert J McCann · 1995
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The quickhull algorithm for convex hulls
C. Bradford Barber, David P. Dobkin, and Hannu Huhdanpaa · 1996
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Justin R. Williams and Catherine M. Crespi · 2008
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Quantile and probability curves without crossing
Victor Chernozhukov, Iván Fernández-Val, and Alfred Galichon · 2010
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Displacement interpolation using Lagrangian mass transport
Nicolas Bonneel, Michiel Van De Panne, Sylvain Paris, and Wolfgang Heidrich · 2011
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Regularized discrete optimal transport
Sira Ferradans, Nicolas Papadakis, Julien Rabin, Gabriel Peyré, and Jean-François Aujol · 2013
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Stochastic first-and zeroth-order methods for nonconvex stochastic programming
Saeed Ghadimi and Guanghui Lan · 2013
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Iterative bregman projections for regularized transportation problems
Jean-David Benamou, Guillaume Carlier, Marco Cuturi, Luca Nenna, and Gabriel Peyré · 2015
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Convolutional wasserstein distances: Efficient optimal transportation on geometric domains
Justin Solomon, Fernando De Goes, Gabriel Peyré, Marco Cuturi, Adrian Butscher, Andy Nguyen, Tao Du, and Leonidas Guibas · 2015
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Vector quantile regression: An optimal transport approach
Guillaume Carlier, Victor Chernozhukov, and Alfred Galichon · 2016
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CVXPY: A Python-embedded modeling language for convex optimization
Steven Diamond and Stephen Boyd · 2016
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Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
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Vector quantile regression beyond the specified case
Pyod: A python toolbox for scalable outlier detection
Yue Zhao, Zain Nasrullah, and Zheng Li · 2019
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Vector quantile regression and optimal transport, from theory to numerics
Guillaume Carlier, Victor Chernozhukov, Gwendoline De Bie, and Alfred Galichon · 2020
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Distribution-free consistent independence tests via center-outward ranks and signs
Hongjian Shi, Mathias Drton, and Fang Han · 2020
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SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python
Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors · 2020
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Kernel operations on the gpu, with autodiff, without memory overflows
Benjamin Charlier, Jean Feydy, Joan Alexis Glaunès, François-David Collin, and Ghislain Durif · 2021
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Guillaume Carlier, Victor Chernozhukov, and Alfred Galichon · 2017
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Victor Chernozhukov, Alfred Galichon, Marc Hallin, and Marc Henry · 2017
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Lecture notes: Optimization for machine learning
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Computational optimal transport
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Conformalized Quantile Regression
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Single-model uncertainties for deep learning
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Calibrated multiple-output quantile regression with representation learning
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Pot: Python optimal transport
Rémi Flamary, Nicolas Courty, Alexandre Gramfort, Mokhtar Z. Alaya, Aurélie Boisbunon, Stanislas Chambon, Laetitia Chapel, Adrien Corenflos, Kilian Fatras, Nemo Fournier, Léo Gautheron, Nathalie T.H. Gayraud, Hicham Janati, Alain Rakotomamonjy, Ievgen Redko, Antoine Rolet, Antony Schutz, Vivien Seguy, Danica J. Sutherland, Romain Tavenard, Alexander Tong, and Titouan Vayer · 2021
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Do neural optimal transport solvers work? a continuous wasserstein-2 benchmark
Alexander Korotin, Lingxiao Li, Aude Genevay, Justin M Solomon, Alexander Filippov, and Evgeny Burnaev · 2021
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Conformal prediction using conditional histograms
Matteo Sesia and Yaniv Romano · 2021
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Topics in optimal transportation , volume 58
Cédric Villani · 2021
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Deep non-crossing quantiles through the partial derivative
Axel Brando, Joan Gimeno, Jose A Rodríguez-Serrano, and Jordi Vitrià · 2022
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