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The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness-of-fit (GoF) statistics.
On the estimation of the discrepancy between empirical curves of distribution for two independent samples
Nikolai V. Smirnov · 1939
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Probability tables for individual comparisons by ranking methods
Frank Wilcoxon · 1947
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The Speed of Mean Glivenko-Cantelli Convergence
R. M. Dudley · 1969
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Colonic inflammation in the rabbit induced by phorbol-12-myristate-13-acetate
D.J. Fretland, D.L. Widomski, S. Levin, and T.S. Gaginella · 1990
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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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Controlling the false discovery rate: a practical and powerful approach to multiple testing
Yoav Benjamini and Yosef Hochberg · 1995
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Serum n3 polyunsaturated fatty acids are depleted in Crohn’s disease
Fumitoshi Kuroki, Mitsuo Iida, Takayuki Matsumoto, Kunihiko Aoyagi, Kohki Kanamoto, and Masatoshi Fujishima · 1997
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Gradient-based learning applied to document recognition
Yann LeCun, Léon Bottou, Yoshua Bengio, and Patrick Haffner · 1998
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On a new multivariate two-sample test
Ludwig Baringhaus and Carsten Franz · 2004
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Convex optimization
Stephen Boyd, Stephen P. Boyd, and Lieven Vandenberghe · 2004
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Hierarchical clustering via joint between-within distances: Extending ward’s minimum variance method
Gabor J Szekely, Maria L Rizzo, et al · 2005
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A kernel statistical test of independence
Arthur Gretton, Kenji Fukumizu, Choon Teo, Le Song, Bernhard Schölkopf, and Alex Smola · 2007
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Softrank: optimizing non-smooth rank metrics
Michael Taylor, John Guiver, Stephen Robertson, and Tom Minka · 2008
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Optimal Transport: Old and New
Cédric Villani · 2009
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On the distribution properties of Niederreiter–Halton sequences
Roswitha Hofer · 2009
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An adaptive step-down procedure with proven fdr control under independence
Yulia Gavrilov, Yoav Benjamini, and Sanat K Sarkar · 2009
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The long journey of salicylates in ulcerative colitis: The past and the future
Renzo Caprilli, Monica Cesarini, Erika Angelucci, and Giuseppe Frieri · 2009
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Genome-wide meta-analysis increases to 71 the number of confirmed crohn’s disease susceptibility loci
Andre Franke, Dermot PB McGovern, Jeffrey C Barrett, Kai Wang, Graham L Radford-Smith, Tariq Ahmad, Charlie W Lees, Tobias Balschun, James Lee, Rebecca Roberts, et al · 2010
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Regularization paths for generalized linear models via coordinate descent
Jerome Friedman, Trevor Hastie, and Rob Tibshirani · 2010
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A gentle introduction to the kernel distance
Jeff M Phillips and Suresh Venkatasubramanian · 2011
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Ranking via Sinkhorn propagation
Ryan Prescott Adams and Richard S Zemel · 2011
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Serum fatty acid profile in subjects with irritable bowel syndrome
Tiina Solakivi, Katri Kaukinen, Tarja Kunnas, Terho Lehtimäki, Markku Mäki, and Seppo Tapio Nikkari · 2011
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A kernel two-sample test
Arthur Gretton, Karsten M Borgwardt, Malte J. Rasch, Bernhard Schölkopf, and Alexander Smola · 2012
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Stochastic gradient descent tricks
Léon Bottou · 2012
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Etiology of inflammatory bowel disease: a unified hypothesis
Xiaofa Qin · 2012
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A consistent multivariate test of association based on ranks of distances
Ruth Heller, Yair Heller, and Malka Gorfine · 2013
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Sinkhorn distances: Lightspeed computation of optimal transport
Marco Cuturi · 2013
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Energy statistics: A class of statistics based on distances
Gábor J Székely and Maria L Rizzo · 2013
Cited alongside, same era.
Concentration inequalities: A nonasymptotic theory of independence
Stéphane Boucheron, Gábor Lugosi, and Pascal Massart · 2013
Cited alongside, same era.
Auto-encoding variational Bayes
Diederik P. Kingma and Max Welling · 2013
Cited alongside, same era.
Generative adversarial networks
Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
Cited alongside, same era.
Computational optimal transport: With applications to data science
Gabriel Peyré, Marco Cuturi, et al · 2019
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Entropy-regularized optimal transport for machine learning
Aude Genevay · 2019
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Differentiable convex optimization layers
Akshay Agrawal, Brandon Amos, Shane Barratt, Stephen Boyd, Steven Diamond, and J. Zico Kolter · 2019
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Interpolating between optimal transport and MMD using Sinkhorn divergences
Jean Feydy, Thibault Séjourné, François-Xavier Vialard, Shun-ichi Amari, Alain Trouvé, and Gabriel Peyré · 2019
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An introduction to variational autoencoders
Diederik P. Kingma and Max Welling · 2019
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Multi-omics of the gut microbial ecosystem in inflammatory bowel diseases
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Filippo Santambrogio · 2015
Cited alongside, same era.
Controlling the false discovery rate via knockoffs
Rina Foygel Barber and Emmanuel J. Candès · 2015
Cited alongside, same era.
Optimal transport for applied mathematicians
Filippo Santambrogio · 2015
Cited alongside, same era.
Generative moment matching networks
Yujia Li, Kevin Swersky, and Rich Zemel · 2015
Cited alongside, same era.
Empirical evaluation of rectified activations in convolutional network
Bing Xu, Naiyan Wang, Tianqi Chen, and Mu Li · 2015
Cited alongside, same era.
Stochastic optimization for large-scale optimal transport
Aude Genevay, Marco Cuturi, Gabriel Peyré, and Francis Bach · 2016
Cited alongside, same era.
Panning for gold: Model-X knockoffs for high-dimensional controlled variable selection
Emmanuel Candes, Yingying Fan, Lucas Janson, and Jinchi Lv · 2016
Cited alongside, same era.
Jason Lloyd-Price, Cesar Arze, Ashwin N Ananthakrishnan, Melanie Schirmer, Julian Avila-Pacheco, Tiffany W Poon, Elizabeth Andrews, Nadim J Ajami, Kevin S Bonham, Colin J Brislawn, et al · 2019
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Elevated faecal 12, 13-dihome concentration in neonates at high risk for asthma is produced by gut bacteria and impedes immune tolerance
Sophia R. Levan, Kelsey A. Stamnes, Din L. Lin, Ariane R. Panzer, Elle Fukui, Kathryn McCauley, Kei E. Fujimura, Michelle McKean, Dennis R. Ownby, Edward M. Zoratti, et al · 2019
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Olmesartan ameliorates chemically-induced ulcerative colitis in rats via modulating NF κ \kappa b and Nrf-2/HO-1 signaling crosstalk
Sameh Saber, Rania M Khalil, Walied S Abdo, Doaa Nassif, and Eman El-Ahwany · 2019
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Sample complexity of Sinkhorn divergences
Aude Genevay, Lénaic Chizat, Francis Bach, Marco Cuturi, and Gabriel Peyré · 2019
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Statistical bounds for entropic optimal transport: Sample complexity and the central limit theorem
Gonzalo Mena and Jonathan Niles-Weed · 2019
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On matched filtering for statistical change point detection
Kevin C. Cheng, Eric L. Miller, Michael C. Hughes, and Shuchin Aeron · 2020
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Fast differentiable sorting and ranking
Mathieu Blondel, Olivier Teboul, Quentin Berthet, and Josip Djolonga · 2020
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Deep knockoffs
Yaniv Romano, Matteo Sesia, and Emmanuel Candès · 2020
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Deep direct likelihood knockoffs
Mukund Sudarshan, Wesley Tansey, and Rajesh Ranganath · 2020
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Gut microbiota-derived metabolites as key actors in inflammatory bowel disease
Aonghus Lavelle and Harry Sokol · 2020
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Faster Wasserstein distance estimation with the Sinkhorn divergence
Lenaic Chizat, Pierre Roussillon, Flavien Léger, François-Xavier Vialard, and Gabriel Peyré · 2020
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Distribution and quantile functions, ranks and signs in dimension d d : A measure transportation approach
Marc Hallin, Eustasio del Barrio, Juan Cuesta-Albertos, and Carlos Matrán · 2021
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Multivariate rank-based distribution-free nonparametric testing using measure transportation
Nabarun Deb and Bodhisattva Sen · 2021
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Measure transportation and statistical decision theory
Marc Hallin · 2021
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Entropic estimation of optimal transport maps
Aram-Alexandre Pooladian and Jonathan Niles-Weed · 2021
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Entropic regularization of continuous optimal transport problems
Christian Clason, Dirk A Lorenz, Hinrich Mahler, and Benedikt Wirth · 2021
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Minimax estimation of smooth optimal transport maps
Jan-Christian Hütter and Philippe Rigollet · 2021
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Predictive metagenomic analysis of autoimmune disease identifies robust autoimmunity and disease specific microbial signatures
Angelina Volkova and Kelly V. Ruggles · 2021
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Metabolomics as a promising resource identifying potential biomarkers for inflammatory bowel disease
Cristina Bauset, Laura Gisbert-Ferrándiz, and Jesús Cosín-Roger · 2021
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On the sample complexity of entropic optimal transport
Philippe Rigollet and Austin J Stromme · 2022
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Debiaser beware: Pitfalls of centering regularized transport maps
Aram-Alexandre Pooladian, Marco Cuturi, and Jonathan Niles-Weed · 2022
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