---
references:
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  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Agueh
      given: Martial
    - family: Carlier
      given: Guillaume
  citation-key: AguehBarycenters2011
  container-title: SIAM Journal on Mathematical Analysis
  container-title-short: SIAM J. Math. Anal.
  DOI: 10.1137/100805741
  ISSN: 0036-1410, 1095-7154
  issue: '2'
  issued:
    - year: 2011
      month: 1
  language: en
  page: 904-924
  title: Barycenters in the Wasserstein Space
  type: article-journal
  volume: '43'

- id: AlayaScreening2019
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Alaya
      given: Mokhtar Z.
    - family: Berar
      given: Maxime
    - family: Gasso
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    - family: Rakotomamonjy
      given: Alain
  citation-key: AlayaScreening2019
  container-title: Advances in Neural Information Processing Systems
  issued:
    - year: 2019
  language: en
  title: Screening Sinkhorn Algorithm for Regularized Optimal Transport
  type: article-journal
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    https://papers.nips.cc/paper/2019/hash/95688ba636a4720a85b3634acfec8cdd-Abstract.html
  volume: '32'

- id: AltschulerNearlinear
  author:
    - family: Altschuler
      given: Jason
    - family: Niles-Weed
      given: Jonathan
    - family: Rigollet
      given: Philippe
  citation-key: AltschulerNearlinear
  issued:
    - year: 2017
  language: en
  page: '11'
  title: >-
    Near-linear time approximation algorithms for optimal transport via Sinkhorn
    iteration
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- id: AmbrogioniWasserstein2018
  accessed:
    - year: 2019
      month: 8
      day: 12
  author:
    - family: Ambrogioni
      given: Luca
    - family: Güçlü
      given: Umut
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      given: Yagmur
    - family: Hinne
      given: Max
    - family: Maris
      given: Eric
    - family: Gerven
      given: Marcel A. J.
      non-dropping-particle: van
  citation-key: AmbrogioniWasserstein2018
  collection-title: NIPS'18
  container-title: >-
    Proceedings of the 32Nd International Conference on Neural Information
    Processing Systems
  event-place: Montréal, Canada
  issued:
    - year: 2018
  page: 2478–2487
  publisher: Curran Associates Inc.
  publisher-place: USA
  title: Wasserstein Variational Inference
  type: paper-conference
  URL: http://arxiv.org/abs/1805.11284

- id: AmbrogioniWasserstein2019
  accessed:
    - year: 2024
      month: 2
      day: 21
  author:
    - family: Ambrogioni
      given: Luca
    - family: Guclu
      given: Umut
    - family: Gerven
      given: Marcel
      non-dropping-particle: van
  citation-key: AmbrogioniWasserstein2019
  DOI: 10.48550/arXiv.1811.02827
  issued:
    - year: 2019
      month: 5
      day: 15
  number: arXiv:1811.02827
  publisher: arXiv
  title: >-
    Wasserstein variational gradient descent: From semi-discrete optimal
    transport to ensemble variational inference
  type: article
  URL: http://arxiv.org/abs/1811.02827

- id: AmbrosioGradient2008
  accessed:
    - year: 2019
      month: 6
      day: 29
  author:
    - family: Ambrosio
      given: Luigi
    - family: Gigli
      given: Nicola
    - family: Savare
      given: Giuseppe
  citation-key: AmbrosioGradient2008
  collection-title: Lectures in Mathematics. ETH Zürich
  edition: '2'
  ISBN: 978-3-7643-8721-1
  issued:
    - year: 2008
  language: en
  publisher: Birkhäuser Basel
  title: 'Gradient Flows: In Metric Spaces and in the Space of Probability Measures'
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- id: AngenentMinimizing2003
  accessed:
    - year: 2021
      month: 6
      day: 9
  author:
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      given: Sigurd
    - family: Haker
      given: Steven
    - family: Tannenbaum
      given: Allen
  citation-key: AngenentMinimizing2003
  container-title: SIAM Journal on Mathematical Analysis
  container-title-short: SIAM J. Math. Anal.
  DOI: 10.1137/S0036141002410927
  ISSN: 0036-1410
  issue: '1'
  issued:
    - year: 2003
      month: 1
      day: 1
  page: 61-97
  publisher: Society for Industrial and Applied Mathematics
  title: Minimizing Flows for the Monge-Kantorovich Problem
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- id: ArjovskyWasserstein2017
  accessed:
    - year: 2018
      month: 9
      day: 24
  author:
    - family: Arjovsky
      given: Martin
    - family: Chintala
      given: Soumith
    - family: Bottou
      given: Léon
  citation-key: ArjovskyWasserstein2017
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 214-223
  title: Wasserstein Generative Adversarial Networks
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/arjovsky17a.html

- id: AroraGeneralization2017
  author:
    - family: Arora
      given: Sanjeev
    - family: Ge
      given: Rong
    - family: Liang
      given: Yingyu
    - family: Ma
      given: Tengyu
    - family: Zhang
      given: Yi
  citation-key: AroraGeneralization2017
  container-title: arXiv:1703.00573 [cs]
  issued:
    - year: 2017
      month: 3
      day: 1
  title: Generalization and Equilibrium in Generative Adversarial Nets (GANs)
  type: article-journal
  URL: http://arxiv.org/abs/1703.00573

- id: BachocGaussian2019
  accessed:
    - year: 2020
      month: 11
      day: 30
  author:
    - family: Bachoc
      given: Francois
    - family: Suvorikova
      given: Alexandra
    - family: Ginsbourger
      given: David
    - family: Loubes
      given: Jean-Michel
    - family: Spokoiny
      given: Vladimir
  citation-key: BachocGaussian2019
  container-title: arXiv:1805.00753 [stat]
  issued:
    - year: 2019
      month: 4
      day: 11
  language: en
  title: >-
    Gaussian processes with multidimensional distribution inputs via optimal
    transport and Hilbertian embedding
  type: article-journal
  URL: http://arxiv.org/abs/1805.00753

- id: BaiLinear2023
  accessed:
    - year: 2023
      month: 5
      day: 3
  author:
    - family: Bai
      given: Yikun
    - family: Medri
      given: Ivan
    - family: Martin
      given: Rocio Diaz
    - family: Khan
      given: Rana Muhammad Shahroz
    - family: Kolouri
      given: Soheil
  citation-key: BaiLinear2023
  issued:
    - year: 2023
      month: 2
      day: 7
  language: en
  title: Linear Optimal Partial Transport Embedding
  type: article
  URL: https://arxiv.org/abs/2302.03232v3

- id: BenamouIterative2014
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
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      given: Jean-David
    - family: Carlier
      given: Guillaume
    - family: Cuturi
      given: Marco
    - family: Nenna
      given: Luca
    - family: Peyré
      given: Gabriel
  citation-key: BenamouIterative2014
  container-title: arXiv:1412.5154 [math]
  issued:
    - year: 2014
      month: 12
      day: 16
  language: en
  title: Iterative Bregman Projections for Regularized Transportation Problems
  type: article-journal
  URL: http://arxiv.org/abs/1412.5154

- id: BenamouOptimal2021
  accessed:
    - year: 2022
      month: 8
      day: 18
  author:
    - family: Benamou
      given: Jean-David
  citation-key: BenamouOptimal2021
  container-title: Acta Numerica
  DOI: 10.1017/S0962492921000040
  ISSN: 0962-4929, 1474-0508
  issued:
    - year: 2021
      month: 5
  language: en
  page: 249-325
  publisher: Cambridge University Press
  title: Optimal transportation, modelling and numerical simulation
  type: article-journal
  volume: '30'

- id: BishopDistributed2014
  accessed:
    - year: 2022
      month: 2
      day: 21
  author:
    - family: Bishop
      given: Adrian N.
    - family: Doucet
      given: Arnaud
  citation-key: BishopDistributed2014
  collection-title: 19th IFAC World Congress
  container-title: IFAC Proceedings Volumes
  container-title-short: IFAC Proceedings Volumes
  DOI: 10.3182/20140824-6-ZA-1003.00341
  ISSN: 1474-6670
  issue: '3'
  issued:
    - year: 2014
      month: 1
      day: 1
  language: en
  page: 8662-8668
  title: Distributed Nonlinear Consensus in the Space of Probability Measures
  type: article-journal
  volume: '47'

- id: BlanchetConfidence2019
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
    - family: Blanchet
      given: Jose
    - family: Murthy
      given: Karthyek
    - family: Si
      given: Nian
  citation-key: BlanchetConfidence2019
  container-title: arXiv:1906.01614 [math, stat]
  issued:
    - year: 2019
      month: 6
      day: 4
  title: Confidence Regions in Wasserstein Distributionally Robust Estimation
  type: article-journal
  URL: http://arxiv.org/abs/1906.01614

- id: BlanchetDistributionally2018
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
    - family: Blanchet
      given: Jose
    - family: Chen
      given: Lin
    - family: Zhou
      given: Xun Yu
  citation-key: BlanchetDistributionally2018
  container-title: arXiv:1802.04885 [stat]
  issued:
    - year: 2018
      month: 2
      day: 13
  title: >-
    Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein
    Distances
  type: article-journal
  URL: http://arxiv.org/abs/1802.04885

- id: BlanchetOptimal2018
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
    - family: Blanchet
      given: Jose
    - family: Murthy
      given: Karthyek
    - family: Zhang
      given: Fan
  citation-key: BlanchetOptimal2018
  container-title: arXiv:1810.02403 [math]
  issued:
    - year: 2018
      month: 10
      day: 4
  title: >-
    Optimal Transport Based Distributionally Robust Optimization: Structural
    Properties and Iterative Schemes
  type: article-journal
  URL: http://arxiv.org/abs/1810.02403

- id: BlanchetOptimal2018
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
    - family: Blanchet
      given: Jose
    - family: Jambulapati
      given: Arun
    - family: Kent
      given: Carson
    - family: Sidford
      given: Aaron
  citation-key: BlanchetOptimal2018
  container-title: arXiv:1810.07717 [cs]
  issued:
    - year: 2018
      month: 10
      day: 17
  title: Towards Optimal Running Times for Optimal Transport
  type: article-journal
  URL: http://arxiv.org/abs/1810.07717

- id: BlanchetRobust2016
  accessed:
    - year: 2019
      month: 7
      day: 9
  author:
    - family: Blanchet
      given: Jose
    - family: Kang
      given: Yang
    - family: Murthy
      given: Karthyek
  citation-key: BlanchetRobust2016
  container-title: arXiv:1610.05627 [math, stat]
  issued:
    - year: 2016
      month: 10
      day: 18
  title: Robust Wasserstein Profile Inference and Applications to Machine Learning
  type: article-journal
  URL: http://arxiv.org/abs/1610.05627

- id: BlondelSmooth2018
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Blondel
      given: Mathieu
    - family: Seguy
      given: Vivien
    - family: Rolet
      given: Antoine
  citation-key: BlondelSmooth2018
  container-title: AISTATS 2018
  event-title: AISTATS
  issued:
    - year: 2018
      month: 2
      day: 20
  title: Smooth and Sparse Optimal Transport
  type: paper-conference
  URL: http://arxiv.org/abs/1710.06276

- id: BoissardSimple2011
  accessed:
    - year: 2021
      month: 5
      day: 17
  author:
    - family: Boissard
      given: Emmanuel
  citation-key: BoissardSimple2011
  container-title: Electronic Journal of Probability
  container-title-short: Electron. J. Probab.
  DOI: 10.1214/EJP.v16-958
  ISSN: 1083-6489
  issue: none
  issued:
    - year: 2011
      month: 1
      day: 1
  language: en
  title: >-
    Simple Bounds for the Convergence of Empirical and Occupation Measures in
    1-Wasserstein Distance
  type: article-journal
  volume: '16'

- id: BonneelDisplacement
  author:
    - family: Bonneel
      given: Nicolas
  citation-key: BonneelDisplacement
  language: en
  page: '11'
  title: Displacement Interpolation Using Lagrangian Mass Transport
  type: article-journal

- id: BonnotteKnothe2012
  accessed:
    - year: 2023
      month: 2
      day: 21
  author:
    - family: Bonnotte
      given: Nicolas
  citation-key: BonnotteKnothe2012
  issued:
    - year: 2012
      month: 9
      day: 25
  publisher: arXiv
  title: From Knothe's rearrangement to Brenier's optimal transport map
  type: thesis
  URL: http://arxiv.org/abs/1205.1099

- id: CanasLearning2012
  accessed:
    - year: 2018
      month: 11
      day: 23
  author:
    - family: Canas
      given: Guillermo D.
    - family: Rosasco
      given: Lorenzo
  citation-key: CanasLearning2012
  container-title: arXiv:1209.1077 [cs, stat]
  issued:
    - year: 2012
      month: 9
      day: 5
  title: Learning Probability Measures with respect to Optimal Transport Metrics
  type: article-journal
  URL: http://arxiv.org/abs/1209.1077

- id: CarlierKnothe2008
  accessed:
    - year: 2023
      month: 2
      day: 20
  author:
    - family: Carlier
      given: Guillaume
    - family: Galichon
      given: Alfred
    - family: Santambrogio
      given: Filippo
  citation-key: CarlierKnothe2008
  DOI: 10.48550/arXiv.0810.4153
  issued:
    - year: 2008
      month: 10
      day: 22
  number: arXiv:0810.4153
  publisher: arXiv
  title: >-
    From Knothe's transport to Brenier's map and a continuation method for
    optimal transport
  type: article
  URL: http://arxiv.org/abs/0810.4153

- id: CarlierOptimal2017
  author:
    - family: Carlier
      given: Guillaume
    - family: Cuturi
      given: Marco
    - family: Pass
      given: Brendan
    - family: Schoenlieb
      given: Carola
  citation-key: CarlierOptimal2017
  issued:
    - year: 2017
  language: en
  page: '9'
  title: Optimal Transport meets Probability, Statistics and Machine Learning
  type: article-journal

- id: CazellesWassersteinFourier2019
  accessed:
    - year: 2023
      month: 11
      day: 15
  author:
    - family: Cazelles
      given: Elsa
    - family: Robert
      given: Arnaud
    - family: Tobar
      given: Felipe
  citation-key: CazellesWassersteinFourier2019
  issued:
    - year: 2019
      month: 12
      day: 11
  language: en
  title: The Wasserstein-Fourier Distance for Stationary Time Series
  type: article
  URL: https://arxiv.org/abs/1912.05509v2

- id: ChizatScaling2017
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Chizat
      given: Lenaic
    - family: Peyré
      given: Gabriel
    - family: Schmitzer
      given: Bernhard
    - family: Vialard
      given: François-Xavier
  citation-key: ChizatScaling2017
  container-title: arXiv:1607.05816 [math]
  issued:
    - year: 2017
      month: 5
      day: 22
  language: en
  title: Scaling Algorithms for Unbalanced Transport Problems
  type: article-journal
  URL: http://arxiv.org/abs/1607.05816

- id: ChuProbability2019
  accessed:
    - year: 2019
      month: 7
      day: 9
  author:
    - family: Chu
      given: Casey
    - family: Blanchet
      given: Jose
    - family: Glynn
      given: Peter
  citation-key: ChuProbability2019
  container-title: ICML
  issued:
    - year: 2019
      month: 1
      day: 30
  title: >-
    Probability Functional Descent: A Unifying Perspective on GANs, Variational
    Inference, and Reinforcement Learning
  type: paper-conference
  URL: http://arxiv.org/abs/1901.10691

- id: CorenflosDifferentiable2021
  accessed:
    - year: 2021
      month: 7
      day: 30
  author:
    - family: Corenflos
      given: Adrien
    - family: Thornton
      given: James
    - family: Deligiannidis
      given: George
    - family: Doucet
      given: Arnaud
  citation-key: CorenflosDifferentiable2021
  container-title: arXiv:2102.07850 [cs, stat]
  issued:
    - year: 2021
      month: 6
      day: 30
  title: Differentiable Particle Filtering via Entropy-Regularized Optimal Transport
  type: article-journal
  URL: http://arxiv.org/abs/2102.07850

- id: CosciaGeneralized2020
  author:
    - family: Coscia
      given: Michele
  citation-key: CosciaGeneralized2020
  issued:
    - year: 2020
  language: en
  page: '11'
  title: Generalized Euclidean Measure to Estimate Network Distances
  type: article-journal

- id: CourtyOptimal2016
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Courty
      given: Nicolas
    - family: Flamary
      given: Rémi
    - family: Tuia
      given: Devis
    - family: Rakotomamonjy
      given: Alain
  citation-key: CourtyOptimal2016
  container-title: arXiv:1507.00504 [cs]
  issued:
    - year: 2016
      month: 6
      day: 22
  language: en
  title: Optimal Transport for Domain Adaptation
  type: article-journal
  URL: http://arxiv.org/abs/1507.00504

- id: CuturiFast2014
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
    - family: Cuturi
      given: Marco
    - family: Doucet
      given: Arnaud
  citation-key: CuturiFast2014
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 1938-7228
  issued:
    - year: 2014
      month: 6
      day: 18
  language: en
  page: 685-693
  publisher: PMLR
  title: Fast Computation of Wasserstein Barycenters
  type: paper-conference
  URL: http://proceedings.mlr.press/v32/cuturi14.html

- id: CuturiOptimal2022
  accessed:
    - year: 2023
      month: 9
      day: 28
  author:
    - family: Cuturi
      given: Marco
    - family: Meng-Papaxanthos
      given: Laetitia
    - family: Tian
      given: Yingtao
    - family: Bunne
      given: Charlotte
    - family: Davis
      given: Geoff
    - family: Teboul
      given: Olivier
  citation-key: CuturiOptimal2022
  DOI: 10.48550/arXiv.2201.12324
  issued:
    - year: 2022
      month: 1
      day: 28
  number: arXiv:2201.12324
  publisher: arXiv
  title: 'Optimal Transport Tools (OTT): A JAX Toolbox for all things Wasserstein'
  type: article
  URL: http://arxiv.org/abs/2201.12324

- id: CuturiSinkhorn2013
  accessed:
    - year: 2019
      month: 5
      day: 29
  author:
    - family: Cuturi
      given: Marco
  citation-key: CuturiSinkhorn2013
  container-title: Advances in Neural Information Processing Systems 26
  event-title: NIPS
  issued:
    - year: 2013
      month: 6
      day: 4
  language: en
  title: >-
    Sinkhorn Distances: Lightspeed Computation of Optimal Transportation
    Distances
  type: paper-conference
  URL: https://arxiv.org/abs/1306.0895v1

- id: FatrasLearning2020
  accessed:
    - year: 2023
      month: 1
      day: 16
  author:
    - family: Fatras
      given: Kilian
    - family: Zine
      given: Younes
    - family: Flamary
      given: Rémi
    - family: Gribonval
      given: Remi
    - family: Courty
      given: Nicolas
  citation-key: FatrasLearning2020
  container-title: >-
    Proceedings of the Twenty Third International Conference on Artificial
    Intelligence and Statistics
  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2020
      month: 6
      day: 3
  language: en
  page: 2131-2141
  publisher: PMLR
  title: 'Learning with minibatch Wasserstein : asymptotic and gradient properties'
  type: paper-conference
  URL: https://proceedings.mlr.press/v108/fatras20a.html

- id: FernholzMises1983
  author:
    - family: Fernholz
      given: Luisa Turrin
  call-number: QA276-280
  citation-key: FernholzMises1983
  collection-number: '19'
  collection-title: Lecture Notes in Statistics
  event-place: New York
  ISBN: 978-0-387-90899-1 978-1-4612-5604-5
  issued:
    - year: 1983
  language: eng
  publisher: Springer
  publisher-place: New York
  title: von Mises calculus for statistical functionals
  type: book

- id: FeydyInterpolating2019
  accessed:
    - year: 2023
      month: 1
      day: 16
  author:
    - family: Feydy
      given: Jean
    - family: Séjourné
      given: Thibault
    - family: Vialard
      given: François-Xavier
    - family: Amari
      given: Shun-ichi
    - family: Trouve
      given: Alain
    - family: Peyré
      given: Gabriel
  citation-key: FeydyInterpolating2019
  container-title: >-
    Proceedings of the Twenty-Second International Conference on Artificial
    Intelligence and Statistics
  event-title: The 22nd International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2019
      month: 4
      day: 11
  language: en
  page: 2681-2690
  publisher: PMLR
  title: Interpolating between Optimal Transport and MMD using Sinkhorn Divergences
  type: paper-conference
  URL: https://proceedings.mlr.press/v89/feydy19a.html

- id: FlamaryOptimal
  author:
    - family: Flamary
      given: Remi
    - family: Rakotomamonjy
      given: Alain
    - family: Courty
      given: Nicolas
    - family: Tuia
      given: Devis
  citation-key: FlamaryOptimal
  language: en
  page: '10'
  title: Optimal transport with Laplacian regularization
  type: article-journal

- id: FlamaryPOT2021
  author:
    - family: Flamary
      given: Rémi
    - family: Courty
      given: Nicolas
    - family: Gramfort
      given: Alexandre
    - family: Alaya
      given: Mokhtar Z.
    - family: Boisbunon
      given: Aurélie
    - family: Chambon
      given: Stanislas
    - family: Chapel
      given: Laetitia
    - family: Corenflos
      given: Adrien
    - family: Fatras
      given: Kilian
    - family: Fournier
      given: Nemo
    - family: Gautheron
      given: Léo
    - family: Gayraud
      given: Nathalie T.H.
    - family: Janati
      given: Hicham
    - family: Rakotomamonjy
      given: Alain
    - family: Redko
      given: Ievgen
    - family: Rolet
      given: Antoine
    - family: Schutz
      given: Antony
    - family: Seguy
      given: Vivien
    - family: Sutherland
      given: Danica J.
    - family: Tavenard
      given: Romain
    - family: Tong
      given: Alexander
    - family: Vayer
      given: Titouan
  citation-key: FlamaryPOT2021
  container-title: Journal of Machine Learning Research
  issue: '78'
  issued:
    - year: 2021
  page: 1-8
  title: 'POT: Python optimal transport'
  type: article-journal
  URL: http://jmlr.org/papers/v22/20-451.html
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- id: FlamaryWasserstein2018
  accessed:
    - year: 2021
      month: 3
      day: 15
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      given: Rémi
    - family: Cuturi
      given: Marco
    - family: Courty
      given: Nicolas
    - family: Rakotomamonjy
      given: Alain
  citation-key: FlamaryWasserstein2018
  container-title: Machine Learning
  container-title-short: Mach Learn
  DOI: 10.1007/s10994-018-5717-1
  ISSN: 0885-6125, 1573-0565
  issue: '12'
  issued:
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      month: 12
  language: en
  page: 1923-1945
  title: Wasserstein Discriminant Analysis
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  URL: http://arxiv.org/abs/1608.08063
  volume: '107'

- id: FrognerLearning2015
  accessed:
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      month: 8
      day: 29
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    - family: Zhang
      given: Chiyuan
    - family: Mobahi
      given: Hossein
    - family: Araya
      given: Mauricio
    - family: Poggio
      given: Tomaso A
  citation-key: FrognerLearning2015
  container-title: Advances in Neural Information Processing Systems 28
  editor:
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      given: C.
    - family: Lawrence
      given: N. D.
    - family: Lee
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    - family: Sugiyama
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    - family: Garnett
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  page: 2053–2061
  publisher: Curran Associates, Inc.
  title: Learning with a Wasserstein Loss
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- id: GaoDistributionally2022
  accessed:
    - year: 2022
      month: 8
      day: 30
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    - family: Kleywegt
      given: Anton J.
  citation-key: GaoDistributionally2022
  DOI: 10.48550/arXiv.1604.02199
  issued:
    - year: 2022
      month: 4
      day: 30
  number: arXiv:1604.02199
  publisher: arXiv
  title: Distributionally Robust Stochastic Optimization with Wasserstein Distance
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- id: GarbunoInigoInteracting2020
  accessed:
    - year: 2020
      month: 7
      day: 23
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      given: Alfredo
    - family: Hoffmann
      given: Franca
    - family: Li
      given: Wuchen
    - family: Stuart
      given: Andrew M.
  citation-key: GarbunoInigoInteracting2020
  container-title: SIAM Journal on Applied Dynamical Systems
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  DOI: 10.1137/19M1251655
  issue: '1'
  issued:
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      month: 1
      day: 1
  page: 412-441
  publisher: Society for Industrial and Applied Mathematics
  title: >-
    Interacting Langevin Diffusions: Gradient Structure and Ensemble Kalman
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  volume: '19'

- id: GenevayLearning2017
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
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      given: Aude
    - family: Peyré
      given: Gabriel
    - family: Cuturi
      given: Marco
  citation-key: GenevayLearning2017
  container-title: arXiv:1706.00292 [stat]
  issued:
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      month: 10
      day: 20
  title: Learning Generative Models with Sinkhorn Divergences
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  URL: http://arxiv.org/abs/1706.00292

- id: GenevayStochastic2016
  author:
    - family: Genevay
      given: Aude
    - family: Cuturi
      given: Marco
    - family: Peyré
      given: Gabriel
    - family: Bach
      given: Francis
  citation-key: GenevayStochastic2016
  container-title: Advances in Neural Information Processing Systems 29
  editor:
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      given: D. D.
    - family: Sugiyama
      given: M.
    - family: Luxburg
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    - family: Guyon
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  page: 3432–3440
  publisher: Curran Associates, Inc.
  title: Stochastic Optimization for Large-scale Optimal Transport
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- id: GoodfellowGenerative2014
  accessed:
    - year: 2018
      month: 12
      day: 30
  author:
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      given: Ian
    - family: Pouget-Abadie
      given: Jean
    - family: Mirza
      given: Mehdi
    - family: Xu
      given: Bing
    - family: Warde-Farley
      given: David
    - family: Ozair
      given: Sherjil
    - family: Courville
      given: Aaron
    - family: Bengio
      given: Yoshua
  citation-key: GoodfellowGenerative2014
  collection-title: NIPS'14
  container-title: Advances in Neural Information Processing Systems 27
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      given: Z.
    - family: Welling
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    - family: Cortes
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    - family: Lawrence
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    - family: Weinberger
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  page: 2672–2680
  publisher: Curran Associates, Inc.
  publisher-place: Cambridge, MA, USA
  title: Generative Adversarial Nets
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- id: GozlanTransport2010
  accessed:
    - year: 2021
      month: 5
      day: 17
  author:
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      given: Nathael
    - family: Léonard
      given: Christian
  citation-key: GozlanTransport2010
  container-title: arXiv:1003.3852 [math]
  issued:
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      month: 3
      day: 19
  title: Transport Inequalities. A Survey
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- id: GulrajaniImproved2017
  accessed:
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      day: 27
  author:
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      given: Ishaan
    - family: Ahmed
      given: Faruk
    - family: Arjovsky
      given: Martin
    - family: Dumoulin
      given: Vincent
    - family: Courville
      given: Aaron
  citation-key: GulrajaniImproved2017
  container-title: arXiv:1704.00028 [cs, stat]
  issued:
    - year: 2017
      month: 3
      day: 31
  language: en
  title: Improved Training of Wasserstein GANs
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  URL: http://arxiv.org/abs/1704.00028

- id: GuoRelaxed2017
  author:
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      given: Xin
    - family: Hong
      given: Johnny
    - family: Lin
      given: Tianyi
    - family: Yang
      given: Nan
  citation-key: GuoRelaxed2017
  container-title: arXiv:1705.07164 [cs, stat]
  issued:
    - year: 2017
      month: 5
      day: 19
  title: Relaxed Wasserstein with Applications to GANs
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  URL: http://arxiv.org/abs/1705.07164

- id: HugginsPASSGLM2017
  accessed:
    - year: 2019
      month: 1
      day: 18
  author:
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      given: Jonathan
    - family: Adams
      given: Ryan P
    - family: Broderick
      given: Tamara
  citation-key: HugginsPASSGLM2017
  container-title: Advances in Neural Information Processing Systems 30
  editor:
    - family: Guyon
      given: I.
    - family: Luxburg
      given: U. V.
    - family: Bengio
      given: S.
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    - family: Fergus
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  issued:
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  page: 3611–3621
  publisher: Curran Associates, Inc.
  title: >-
    PASS-GLM: polynomial approximate sufficient statistics for scalable Bayesian
    GLM inference
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  URL: >-
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- id: HugginsPractical2018
  accessed:
    - year: 2019
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      day: 18
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      given: Jonathan H.
    - family: Campbell
      given: Trevor
    - family: Kasprzak
      given: Mikołaj
    - family: Broderick
      given: Tamara
  citation-key: HugginsPractical2018
  container-title: arXiv:1809.09505 [cs, math, stat]
  issued:
    - year: 2018
      month: 9
      day: 25
  title: >-
    Practical bounds on the error of Bayesian posterior approximations: A
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  URL: http://arxiv.org/abs/1809.09505

- id: HugginsPractical2019
  accessed:
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      month: 10
      day: 11
  author:
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      given: Jonathan H.
    - family: Kasprzak
      given: Mikołaj
    - family: Campbell
      given: Trevor
    - family: Broderick
      given: Tamara
  citation-key: HugginsPractical2019
  container-title: arXiv:1910.04102 [cs, math, stat]
  issued:
    - year: 2019
      month: 10
      day: 9
  title: Practical Posterior Error Bounds from Variational Objectives
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  URL: http://arxiv.org/abs/1910.04102

- id: HugginsScalable2018
  accessed:
    - year: 2019
      month: 1
      day: 18
  author:
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      given: Jonathan H.
    - family: Campbell
      given: Trevor
    - family: Kasprzak
      given: Mikołaj
    - family: Broderick
      given: Tamara
  citation-key: HugginsScalable2018
  container-title: arXiv:1806.10234 [cs, stat]
  issued:
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      month: 6
      day: 26
  title: >-
    Scalable Gaussian Process Inference with Finite-data Mean and Variance
    Guarantees
  type: article-journal
  URL: http://arxiv.org/abs/1806.10234

- id: HuynhOTLDA2020
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    - year: 2023
      month: 10
      day: 26
  author:
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      given: Viet
    - family: Zhao
      given: He
    - family: Phung
      given: Dinh
  citation-key: HuynhOTLDA2020
  container-title: Advances in Neural Information Processing Systems
  issued:
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  page: 18573–18582
  publisher: Curran Associates, Inc.
  title: 'OTLDA: A Geometry-aware Optimal Transport Approach for Topic Modeling'
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  URL: >-
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  volume: '33'

- id: KhanWhen2022
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    - year: 2022
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      day: 5
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      given: Gabriel
    - family: Zhang
      given: Jun
  citation-key: KhanWhen2022
  container-title: Information Geometry
  container-title-short: Info. Geo.
  DOI: 10.1007/s41884-022-00066-w
  ISSN: 2511-249X
  issued:
    - year: 2022
      month: 6
      day: 30
  language: en
  title: When optimal transport meets information geometry
  type: article-journal

- id: KimOptimal2019
  accessed:
    - year: 2020
      month: 7
      day: 23
  author:
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      given: Jin W.
    - family: Mehta
      given: Prashant G.
  citation-key: KimOptimal2019
  issued:
    - year: 2019
      month: 4
      day: 2
  language: en
  title: An Optimal Control Derivation of Nonlinear Smoothing Equations
  type: article-journal
  URL: https://arxiv.org/abs/1904.01710v1

- id: LeonardSurvey2014
  accessed:
    - year: 2020
      month: 7
      day: 23
  author:
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      given: Christian
  citation-key: LeonardSurvey2014
  container-title: Discrete & Continuous Dynamical Systems - A
  DOI: 10.3934/dcds.2014.34.1533
  issue: '4'
  issued:
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  language: en
  page: '1533'
  publisher: American Institute of Mathematical Sciences
  title: >-
    A survey of the Schrödinger problem and some of its connections with optimal
    transport
  type: article-journal
  URL: https://arxiv.org/abs/1308.0215v1
  volume: '34'

- id: LiuStein2019
  accessed:
    - year: 2019
      month: 11
      day: 11
  author:
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      given: Qiang
    - family: Wang
      given: Dilin
  citation-key: LiuStein2019
  container-title: Advances In Neural Information Processing Systems
  event-title: NIPS 2016
  issued:
    - year: 2019
      month: 9
      day: 9
  title: >-
    Stein Variational Gradient Descent: A general purpose Bayesian inference
    algorithm
  type: paper-conference
  URL: http://arxiv.org/abs/1608.04471

- id: LiuTwoStep2018
  accessed:
    - year: 2019
      month: 10
      day: 14
  author:
    - family: Liu
      given: Huidong
    - family: Gu
      given: Xianfeng
    - family: Samaras
      given: Dimitris
  citation-key: LiuTwoStep2018
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  issued:
    - year: 2018
      month: 7
      day: 3
  language: en
  page: 3159-3168
  title: A Two-Step Computation of the Exact GAN Wasserstein Distance
  type: paper-conference
  URL: http://proceedings.mlr.press/v80/liu18d.html

- id: LouizosMultiplicative2017
  author:
    - family: Louizos
      given: Christos
    - family: Welling
      given: Max
  citation-key: LouizosMultiplicative2017
  container-title: PMLR
  event-title: International Conference on Machine Learning
  issued:
    - year: 2017
      month: 7
      day: 17
  language: en
  page: 2218-2227
  title: Multiplicative Normalizing Flows for Variational Bayesian Neural Networks
  type: paper-conference
  URL: http://proceedings.mlr.press/v70/louizos17a.html

- id: MagyarWasserstein2022
  accessed:
    - year: 2022
      month: 12
      day: 12
  author:
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      given: Jared C.
    - family: Sambridge
      given: Malcolm S.
  citation-key: MagyarWasserstein2022
  DOI: 10.5194/egusphere-2022-1117
  genre: preprint
  issued:
    - year: 2022
      month: 11
      day: 10
  language: en
  publisher: Catchment hydrology/Mathematical applications
  title: The Wasserstein distance as a hydrological objective function
  type: report
  URL: https://egusphere.copernicus.org/preprints/2022/egusphere-2022-1117/

- id: MahdianOptimal2019
  accessed:
    - year: 2019
      month: 7
      day: 9
  author:
    - family: Mahdian
      given: Saied
    - family: Blanchet
      given: Jose
    - family: Glynn
      given: Peter
  citation-key: MahdianOptimal2019
  container-title: arXiv:1906.03317 [cs, math, stat]
  issued:
    - year: 2019
      month: 6
      day: 7
  language: en
  title: Optimal Transport Relaxations with Application to Wasserstein GANs
  type: article-journal
  URL: https://arxiv.org/abs/1906.03317v1

- id: MallastoEntropyregularized2021
  accessed:
    - year: 2022
      month: 7
      day: 5
  author:
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      given: Anton
    - family: Gerolin
      given: Augusto
    - family: Minh
      given: Hà Quang
  citation-key: MallastoEntropyregularized2021
  container-title: Information Geometry
  container-title-short: Info. Geo.
  DOI: 10.1007/s41884-021-00052-8
  ISSN: 2511-249X
  issued:
    - year: 2021
      month: 8
      day: 16
  language: en
  title: Entropy-regularized 2-Wasserstein distance between Gaussian measures
  type: article-journal

- id: MarzoukSampling2016
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
    - family: Marzouk
      given: Youssef
    - family: Moselhy
      given: Tarek
    - family: Parno
      given: Matthew
    - family: Spantini
      given: Alessio
  citation-key: MarzoukSampling2016
  container-title: Handbook of Uncertainty Quantification
  DOI: 10.1007/978-3-319-11259-6_23-1
  editor:
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      given: Roger
    - family: Higdon
      given: David
    - family: Owhadi
      given: Houman
  event-place: Cham
  ISBN: 978-3-319-11259-6
  issued:
    - year: 2016
  language: en
  page: 1-41
  publisher: Springer Heidelberg
  publisher-place: Cham
  title: 'Sampling via Measure Transport: An Introduction'
  type: chapter
  URL: https://arxiv.org/abs/1602.05023v1
  volume: '1'

- id: MauryaOptimal2018
  author:
    - family: Maurya
      given: Abhinav
  citation-key: MauryaOptimal2018
  issued:
    - year: 2018
  title: >-
    Optimal Transport in Statistical Machine Learning : Selected Review and Some
    Open Questions
  type: paper-conference

- id: MinhFinite2022
  accessed:
    - year: 2022
      month: 2
      day: 28
  author:
    - family: Minh
      given: Hà Quang
  citation-key: MinhFinite2022
  container-title: SIAM/ASA Journal on Uncertainty Quantification
  container-title-short: SIAM/ASA J. Uncertainty Quantification
  DOI: 10.1137/21M1410488
  issued:
    - year: 2022
      month: 2
      day: 7
  page: 96-124
  publisher: Society for Industrial and Applied Mathematics
  title: >-
    Finite Sample Approximations of Exact and Entropic Wasserstein Distances
    Between Covariance Operators and Gaussian Processes
  type: article-journal

- id: MohajerinEsfahaniDatadriven2018
  accessed:
    - year: 2018
      month: 8
      day: 29
  author:
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      given: Peyman
    - family: Kuhn
      given: Daniel
  citation-key: MohajerinEsfahaniDatadriven2018
  container-title: Mathematical Programming
  container-title-short: Math. Program.
  DOI: 10.1007/s10107-017-1172-1
  ISSN: 1436-4646
  issue: '1'
  issued:
    - year: 2018
      month: 9
      day: 1
  language: en
  page: 115-166
  title: >-
    Data-driven distributionally robust optimization using the Wasserstein
    metric: performance guarantees and tractable reformulations
  type: article-journal
  volume: '171'

- id: MontavonWasserstein2016
  author:
    - family: Montavon
      given: Grégoire
    - family: Müller
      given: Klaus-Robert
    - family: Cuturi
      given: Marco
  citation-key: MontavonWasserstein2016
  container-title: Advances in Neural Information Processing Systems 29
  editor:
    - family: Lee
      given: D. D.
    - family: Sugiyama
      given: M.
    - family: Luxburg
      given: U. V.
    - family: Guyon
      given: I.
    - family: Garnett
      given: R.
  issued:
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  page: 3711–3719
  publisher: Curran Associates, Inc.
  title: Wasserstein Training of Restricted Boltzmann Machines
  type: chapter
  URL: >-
    http://papers.nips.cc/paper/6248-wasserstein-training-of-restricted-boltzmann-machines.pdf

- id: OstrovskiAutoregressive
  author:
    - family: Ostrovski
      given: Georg
    - family: Dabney
      given: Will
    - family: Munos
      given: Remi
  citation-key: OstrovskiAutoregressive
  language: en
  page: '10'
  title: Autoregressive Quantile Networks for Generative Modeling
  type: article-journal

- id: PanaretosStatistical2019
  accessed:
    - year: 2019
      month: 3
      day: 24
  author:
    - family: Panaretos
      given: Victor M.
    - family: Zemel
      given: Yoav
  citation-key: PanaretosStatistical2019
  container-title: Annual Review of Statistics and Its Application
  DOI: 10.1146/annurev-statistics-030718-104938
  issue: '1'
  issued:
    - year: 2019
  page: 405-431
  title: Statistical Aspects of Wasserstein Distances
  type: article-journal
  URL: http://arxiv.org/abs/1806.05500
  volume: '6'

- id: PerrotMapping
  author:
    - family: Perrot
      given: Michaël
    - family: Courty
      given: Nicolas
    - family: Flamary
      given: Rémi
    - family: Habrard
      given: Amaury
  citation-key: PerrotMapping
  language: en
  page: '9'
  title: Mapping Estimation for Discrete Optimal Transport
  type: article-journal

- id: PeyreComputational2019
  accessed:
    - year: 2019
      month: 6
      day: 28
  author:
    - family: Peyré
      given: Gabriel
    - family: Cuturi
      given: Marco
  citation-key: PeyreComputational2019
  DOI: 10.1561/2200000073
  issued:
    - year: 2019
      month: 2
      day: 12
  language: English
  title: Computational Optimal Transport
  type: book
  URL: http://arxiv.org/abs/1803.00567
  volume: '11'

- id: PeyreGromovWasserstein2016
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
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      given: Gabriel
    - family: Cuturi
      given: Marco
    - family: Solomon
      given: Justin
  citation-key: PeyreGromovWasserstein2016
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 1938-7228
  issued:
    - year: 2016
      month: 6
      day: 11
  language: en
  page: 2664-2672
  publisher: PMLR
  title: Gromov-Wasserstein Averaging of Kernel and Distance Matrices
  type: paper-conference
  URL: http://proceedings.mlr.press/v48/peyre16.html

- id: QianNonnegative2016
  accessed:
    - year: 2023
      month: 10
      day: 25
  author:
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      given: Wei
    - family: Hong
      given: Bin
    - family: Cai
      given: Deng
    - family: He
      given: Xiaofei
    - family: Li
      given: Xuelong
  citation-key: QianNonnegative2016
  collection-title: IJCAI'16
  container-title: >-
    Proceedings of the Twenty-Fifth International Joint Conference on Artificial
    Intelligence
  event-place: New York, New York, USA
  ISBN: 978-1-57735-770-4
  issued:
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      month: 7
      day: 9
  page: 1960–1966
  publisher: AAAI Press
  publisher-place: New York, New York, USA
  title: Non-negative matrix factorization with sinkhorn distance
  type: paper-conference
  URL: https://www.ijcai.org/Proceedings/16/Papers/280.pdf

- id: RedkoOptimal2019
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
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      given: Ievgen
    - family: Courty
      given: Nicolas
    - family: Flamary
      given: Rémi
    - family: Tuia
      given: Devis
  citation-key: RedkoOptimal2019
  container-title: The 22nd International Conference on Artificial Intelligence and Statistics
  event-title: The 22nd International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2019
      month: 4
      day: 11
  language: en
  page: 849-858
  publisher: PMLR
  title: Optimal Transport for Multi-source Domain Adaptation under Target Shift
  type: paper-conference
  URL: http://proceedings.mlr.press/v89/redko19a.html

- id: RezendeVariational2015
  accessed:
    - year: 2018
      month: 4
      day: 15
  author:
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      given: Danilo Jimenez
    - family: Mohamed
      given: Shakir
  citation-key: RezendeVariational2015
  collection-title: ICML'15
  container-title: International Conference on Machine Learning
  event-place: Lille, France
  event-title: International Conference on Machine Learning
  issued:
    - year: 2015
      month: 6
      day: 1
  language: en
  page: 1530-1538
  publisher: JMLR.org
  publisher-place: Lille, France
  title: Variational Inference with Normalizing Flows
  type: paper-conference
  URL: http://arxiv.org/abs/1505.05770

- id: RigolletEntropic2018
  accessed:
    - year: 2022
      month: 7
      day: 26
  author:
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      given: Philippe
    - family: Weed
      given: Jonathan
  citation-key: RigolletEntropic2018
  issued:
    - year: 2018
      month: 9
      day: 18
  language: en
  number: arXiv:1809.05572
  publisher: arXiv
  title: Entropic optimal transport is maximum-likelihood deconvolution
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  URL: http://arxiv.org/abs/1809.05572

- id: RustamovClosedform2021
  accessed:
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      month: 5
      day: 3
  author:
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      given: Raif M.
  citation-key: RustamovClosedform2021
  container-title: Stat
  DOI: 10.1002/sta4.329
  ISSN: 2049-1573
  issue: '1'
  issued:
    - year: 2021
  language: en
  page: e329
  title: >-
    Closed-form expressions for maximum mean discrepancy with applications to
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  volume: '10'

- id: SalimansImproving2018
  accessed:
    - year: 2023
      month: 1
      day: 16
  author:
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      given: Tim
    - family: Zhang
      given: Han
    - family: Radford
      given: Alec
    - family: Metaxas
      given: Dimitris
  citation-key: SalimansImproving2018
  DOI: 10.48550/arXiv.1803.05573
  issued:
    - year: 2018
      month: 3
      day: 14
  number: arXiv:1803.05573
  publisher: arXiv
  title: Improving GANs Using Optimal Transport
  type: article
  URL: http://arxiv.org/abs/1803.05573

- id: SambridgeGeophysical2022
  accessed:
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      month: 12
      day: 20
  author:
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      given: Malcolm
    - family: Jackson
      given: Andrew
    - family: Valentine
      given: Andrew P
  citation-key: SambridgeGeophysical2022
  container-title: Geophysical Journal International
  container-title-short: Geophysical Journal International
  DOI: 10.1093/gji/ggac151
  ISSN: 0956-540X
  issue: '1'
  issued:
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      month: 10
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  title: Geophysical inversion and optimal transport
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  volume: '231'

- id: SantambrogioOptimal2015
  accessed:
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      month: 10
      day: 7
  author:
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  citation-key: SantambrogioOptimal2015
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  DOI: 10.1007/978-3-319-20828-2_1
  editor:
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      given: Filippo
  event-place: Cham
  ISBN: 978-3-319-20828-2
  issued:
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  language: en
  publisher: Springer International Publishing
  publisher-place: Cham
  title: Optimal Transport for Applied Mathematicians
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- id: ScetbonLowRank2021
  accessed:
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      month: 10
      day: 26
  author:
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      given: Meyer
    - family: Cuturi
      given: Marco
    - family: Peyré
      given: Gabriel
  citation-key: ScetbonLowRank2021
  container-title: Proceedings of the 38th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2021
      month: 7
      day: 1
  language: en
  page: 9344-9354
  publisher: PMLR
  title: Low-Rank Sinkhorn Factorization
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- id: SchmitzerStabilized2019
  accessed:
    - year: 2021
      month: 3
      day: 15
  author:
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      given: Bernhard
  citation-key: SchmitzerStabilized2019
  container-title: arXiv:1610.06519 [cs, math]
  issued:
    - year: 2019
      month: 2
      day: 11
  language: en
  title: >-
    Stabilized Sparse Scaling Algorithms for Entropy Regularized Transport
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  type: article-journal
  URL: http://arxiv.org/abs/1610.06519

- id: SchmitzWasserstein2018
  accessed:
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      month: 10
      day: 26
  author:
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      given: Morgan A.
    - family: Heitz
      given: Matthieu
    - family: Bonneel
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    - family: Ngolè
      given: Fred
    - family: Coeurjolly
      given: David
    - family: Cuturi
      given: Marco
    - family: Peyré
      given: Gabriel
    - family: Starck
      given: Jean-Luc
  citation-key: SchmitzWasserstein2018
  container-title: SIAM Journal on Imaging Sciences
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  DOI: 10.1137/17M1140431
  ISSN: 1936-4954
  issue: '1'
  issued:
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      month: 1
  language: en
  page: 643-678
  title: >-
    Wasserstein Dictionary Learning: Optimal Transport-Based Unsupervised
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  volume: '11'

- id: SolomonConvolutional2015
  accessed:
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      month: 8
      day: 29
  author:
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      non-dropping-particle: de
    - family: Peyré
      given: Gabriel
    - family: Cuturi
      given: Marco
    - family: Butscher
      given: Adrian
    - family: Nguyen
      given: Andy
    - family: Du
      given: Tao
    - family: Guibas
      given: Leonidas
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  container-title: ACM Transactions on Graphics
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  title: >-
    Convolutional Wasserstein Distances: Efficient Optimal Transportation on
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- id: SpantiniInference2017
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    - family: Marzouk
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  citation-key: SpantiniInference2017
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  issue: '66'
  issued:
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- id: TaghvaeiOptimal2021
  author:
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      given: Amirhossein
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  citation-key: TaghvaeiOptimal2021
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  title: An Optimal Transport Formulation of the Ensemble Kalman Filter
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- id: vandenBergSylvester2018
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    - family: Hasenclever
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    - family: Welling
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  citation-key: vandenBergSylvester2018
  container-title: UAI18
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      day: 15
  title: Sylvester Normalizing Flows for Variational Inference
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- id: VerdinelliHybrid2019
  accessed:
    - year: 2020
      month: 11
      day: 20
  author:
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    - family: Wasserman
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  citation-key: VerdinelliHybrid2019
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  publisher: The Institute of Mathematical Statistics and the Bernoulli Society
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- id: ViehmannImplementation2019
  accessed:
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  citation-key: ViehmannImplementation2019
  DOI: 10.48550/arXiv.1907.01729
  issued:
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      month: 7
      day: 5
  number: arXiv:1907.01729
  publisher: arXiv
  title: >-
    Implementation of batched Sinkhorn iterations for entropy-regularized
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- id: WangLinear2013
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  language: en
  page: 254-269
  PMCID: PMC3667970
  PMID: '23729991'
  title: >-
    A Linear Optimal Transportation Framework for Quantifying and Visualizing
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- id: WangProjected2021
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      day: 21
  author:
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      given: Yifei
    - family: Chen
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  citation-key: WangProjected2021
  DOI: 10.48550/arXiv.2102.06350
  issued:
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      day: 14
  number: arXiv:2102.06350
  publisher: arXiv
  title: >-
    Projected Wasserstein gradient descent for high-dimensional Bayesian
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- id: WangRiemannian2019
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      month: 8
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    - family: Wang
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  citation-key: WangRiemannian2019
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    Proceedings of the 2019 Conference of the North American Chapter of the
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  page: 284–294
  publisher: Association for Computational Linguistics
  publisher-place: Minneapolis, Minnesota
  title: >-
    Riemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text
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- id: ZhangQuantile2020
  accessed:
    - year: 2020
      month: 12
      day: 1
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    - family: Walder
      given: Christian
    - family: Bonilla
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    - family: Rizoiu
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    - family: Xie
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  citation-key: ZhangQuantile2020
  container-title: Proceedings of NeurIPS 2020
  event-title: Neural Information Processing Systems Online Conference 2020
  issued:
    - year: 2020
      month: 12
  language: en
  title: Quantile Propagation for Wasserstein-Approximate Gaussian Processes
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- id: ZhangUnified2021
  accessed:
    - year: 2023
      month: 10
      day: 26
  author:
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  citation-key: ZhangUnified2021
  issued:
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      month: 7
      day: 14
  language: en
  number: arXiv:2104.01708
  publisher: arXiv
  title: >-
    A unified framework for non-negative matrix and tensor factorisations with a
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  type: article
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- id: ZhaoNeural2020
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    - family: Phung
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    - family: Huynh
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    - family: Le
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    - family: Buntine
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  citation-key: ZhaoNeural2020
  event-title: International Conference on Learning Representations
  issued:
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      month: 10
      day: 2
  language: en
  title: Neural Topic Model via Optimal Transport
  type: paper-conference
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- id: ZhuDeconstructing2020
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  citation-key: ZhuDeconstructing2020
  container-title: IEEE Transactions on Information Theory
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  issued:
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  title: Deconstructing Generative Adversarial Networks
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...
