---
references:
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      day: 12
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    - family: Maris
      given: Eric
    - family: Gerven
      given: Marcel A. J.
      non-dropping-particle: van
  citation-key: AmbrogioniWasserstein2018
  collection-title: NIPS'18
  container-title: >-
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    Processing Systems
  event-place: Montréal, Canada
  issued:
    - year: 2018
  page: 2478–2487
  publisher: Curran Associates Inc.
  publisher-place: USA
  title: Wasserstein Variational Inference
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- 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: >-
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  URL: http://arxiv.org/abs/1811.02827

- id: ArjovskyWasserstein2017
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      month: 9
      day: 24
  author:
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    - family: Bottou
      given: Léon
  citation-key: ArjovskyWasserstein2017
  container-title: International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  issued:
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      month: 7
      day: 17
  language: en
  page: 214-223
  title: Wasserstein Generative Adversarial Networks
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- id: BeranMinimum1977
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  citation-key: BeranMinimum1977
  container-title: The Annals of Statistics
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  language: EN
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  accessed:
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      day: 29
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  ISSN: 1467-9868
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- id: BlanchetDatadriven2017
  accessed:
    - year: 2019
      month: 7
      day: 17
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      given: Jose
    - family: Kang
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  container-title: arXiv:1705.07152 [stat]
  issued:
    - year: 2017
      month: 5
      day: 19
  title: Data-driven Optimal Cost Selection for Distributionally Robust Optimization
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- id: BlanchetOptimal2018
  accessed:
    - year: 2019
      month: 7
      day: 17
  author:
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      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: BlanchetRobust2016
  accessed:
    - year: 2019
      month: 7
      day: 9
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      given: Jose
    - family: Kang
      given: Yang
    - family: Murthy
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  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
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- id: BlockSocial2020
  accessed:
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      day: 27
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  container-title: arXiv:2004.07052 [physics, q-bio, stat]
  issued:
    - year: 2020
      month: 4
      day: 15
  title: >-
    Social network-based distancing strategies to flatten the COVID 19 curve in
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- id: CampbellAutomated2017
  accessed:
    - year: 2019
      month: 1
      day: 18
  author:
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      given: Trevor
    - family: Broderick
      given: Tamara
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  container-title: arXiv:1710.05053 [cs, stat]
  issued:
    - year: 2017
      month: 10
      day: 13
  title: Automated Scalable Bayesian Inference via Hilbert Coresets
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- id: ChenMeta2019
  accessed:
    - year: 2019
      month: 3
      day: 4
  author:
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      given: Xinshi
    - family: Dai
      given: Hanjun
    - family: Song
      given: Le
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  container-title: arXiv:1902.00640 [cs, stat]
  issued:
    - year: 2019
      month: 2
      day: 1
  title: Meta Particle Flow for Sequential Bayesian Inference
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- id: ChuProbability2019
  accessed:
    - year: 2019
      month: 7
      day: 9
  author:
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      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
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- id: DellaportaRobust2022
  accessed:
    - year: 2022
      month: 4
      day: 28
  author:
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      given: Charita
    - family: Knoblauch
      given: Jeremias
    - family: Damoulas
      given: Theodoros
    - family: Briol
      given: François-Xavier
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  container-title: arXiv:2202.04744 [cs, stat]
  issued:
    - year: 2022
      month: 2
      day: 23
  title: >-
    Robust Bayesian Inference for Simulator-based Models via the MMD Posterior
    Bootstrap
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- 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:
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  language: eng
  publisher: Springer
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  title: von Mises calculus for statistical functionals
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- id: FernholzStatistical2014
  accessed:
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      month: 10
      day: 7
  author:
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      given: Luisa Turrin
  citation-key: FernholzStatistical2014
  container-title: 'Wiley StatsRef: Statistics Reference Online'
  DOI: 10.1002/9781118445112.stat01843
  ISBN: 978-1-118-44511-2
  issued:
    - year: 2014
  language: en
  publisher: American Cancer Society
  title: Statistical Functionals
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- id: FongScalable2019
  accessed:
    - year: 2022
      month: 4
      day: 28
  author:
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      given: Edwin
    - family: Lyddon
      given: Simon
    - family: Holmes
      given: Chris
  citation-key: FongScalable2019
  container-title: arXiv:1902.03175 [cs, stat]
  issued:
    - year: 2019
      month: 8
      day: 25
  title: >-
    Scalable Nonparametric Sampling from Multimodal Posteriors with the
    Posterior Bootstrap
  type: article-journal
  URL: http://arxiv.org/abs/1902.03175

- id: FrognerLearning2015
  accessed:
    - year: 2018
      month: 8
      day: 29
  author:
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      given: Charlie
    - 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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  issued:
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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
  author:
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      given: Rui
    - 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
  type: article
  URL: http://arxiv.org/abs/1604.02199

- id: GibbsChoosing2002
  accessed:
    - year: 2018
      month: 8
      day: 12
  author:
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      given: Alison L.
    - family: Su
      given: Francis Edward
  citation-key: GibbsChoosing2002
  container-title: International Statistical Review
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  issued:
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      month: 12
      day: 1
  language: en
  page: 419-435
  title: On Choosing and Bounding Probability Metrics
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- id: GulrajaniImproved2017
  accessed:
    - year: 2019
      month: 5
      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
  type: article-journal
  URL: http://arxiv.org/abs/1704.00028

- id: GuoRelaxed2017
  author:
    - family: Guo
      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
  type: article-journal
  URL: http://arxiv.org/abs/1705.07164

- id: LiuKernelized2016
  author:
    - family: Liu
      given: Qiang
    - family: Lee
      given: Jason D
    - family: Jordan
      given: Michael
  citation-key: LiuKernelized2016
  container-title: Proceedings of The 33rd International Conference on Machine Learning
  issued:
    - year: 2016
  language: en
  page: '9'
  title: A Kernelized Stein Discrepancy for Goodness-of-fit Tests
  type: paper-conference
  URL: http://arxiv.org/abs/1602.03253

- 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: LyddonNonparametric2018
  accessed:
    - year: 2022
      month: 4
      day: 27
  author:
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      given: Simon
    - family: Walker
      given: Stephen
    - family: Holmes
      given: Chris
  citation-key: LyddonNonparametric2018
  collection-title: NIPS'18
  container-title: >-
    Proceedings of the 32nd International Conference on Neural Information
    Processing Systems
  event-place: Red Hook, NY, USA
  issued:
    - year: 2018
      month: 12
      day: 3
  page: 2075–2085
  publisher: Curran Associates Inc.
  publisher-place: Red Hook, NY, USA
  title: >-
    Nonparametric learning from Bayesian models with randomized objective
    functions
  type: paper-conference
  URL: http://arxiv.org/abs/1806.11544

- 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: MatsubaraRobust2021
  accessed:
    - year: 2021
      month: 4
      day: 19
  author:
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      given: Takuo
    - family: Knoblauch
      given: Jeremias
    - family: Briol
      given: François-Xavier
    - family: Oates
      given: Chris J.
  citation-key: MatsubaraRobust2021
  container-title: arXiv:2104.07359 [math, stat]
  issued:
    - year: 2021
      month: 4
      day: 15
  language: en
  title: Robust Generalised Bayesian Inference for Intractable Likelihoods
  type: article-journal
  URL: https://arxiv.org/abs/2104.07359v1

- id: MoosmullerLinear2021
  accessed:
    - year: 2021
      month: 7
      day: 6
  author:
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      given: Caroline
    - family: Cloninger
      given: Alexander
  citation-key: MoosmullerLinear2021
  container-title: arXiv:2008.09165 [cs, math, stat]
  issued:
    - year: 2021
      month: 5
      day: 25
  language: en
  title: >-
    Linear Optimal Transport Embedding: Provable Wasserstein classification for
    certain rigid transformations and perturbations
  type: article-journal
  URL: http://arxiv.org/abs/2008.09165

- 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: PacchiardiGeneralized2022
  accessed:
    - year: 2022
      month: 4
      day: 28
  author:
    - family: Pacchiardi
      given: Lorenzo
    - family: Dutta
      given: Ritabrata
  citation-key: PacchiardiGeneralized2022
  container-title: arXiv:2104.03889 [stat]
  issued:
    - year: 2022
      month: 3
      day: 15
  title: >-
    Generalized Bayesian Likelihood-Free Inference Using Scoring Rules
    Estimators
  type: article-journal
  URL: http://arxiv.org/abs/2104.03889

- id: PanaretosStatistical2019
  accessed:
    - year: 2019
      month: 3
      day: 24
  author:
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      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: RanganathOperator2016
  author:
    - family: Ranganath
      given: Rajesh
    - family: Tran
      given: Dustin
    - family: Altosaar
      given: Jaan
    - family: Blei
      given: David
  citation-key: RanganathOperator2016
  container-title: Advances in Neural Information Processing Systems 29
  editor:
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      given: D. D.
    - family: Sugiyama
      given: M.
    - family: Luxburg
      given: U. V.
    - family: Guyon
      given: I.
    - family: Garnett
      given: R.
  issued:
    - year: 2016
  page: 496–504
  publisher: Curran Associates, Inc.
  title: Operator Variational Inference
  type: paper-conference
  URL: http://papers.nips.cc/paper/6091-operator-variational-inference.pdf

- id: RustamovClosedform2021
  accessed:
    - year: 2023
      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
    Wasserstein auto-encoders
  type: article-journal
  URL: http://arxiv.org/abs/1901.03227
  volume: '10'

- id: SantambrogioOptimal2015
  accessed:
    - year: 2019
      month: 10
      day: 7
  author:
    - family: Santambrogio
      given: Filippo
  citation-key: SantambrogioOptimal2015
  collection-title: Progress in Nonlinear Differential Equations and Their Applications
  DOI: 10.1007/978-3-319-20828-2_1
  editor:
    - family: Santambrogio
      given: Filippo
  event-place: Cham
  ISBN: 978-3-319-20828-2
  issued:
    - year: 2015
  language: en
  publisher: Springer International Publishing
  publisher-place: Cham
  title: Optimal Transport for Applied Mathematicians
  type: book
  URL: http://www.math.toronto.edu/~mccann/assignments/477/Santambrogio15.pdf

- id: SchmonGeneralized2021
  accessed:
    - year: 2022
      month: 4
      day: 28
  author:
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      given: Sebastian M.
    - family: Cannon
      given: Patrick W.
    - family: Knoblauch
      given: Jeremias
  citation-key: SchmonGeneralized2021
  container-title: arXiv:2011.08644 [stat]
  issued:
    - year: 2021
      month: 2
      day: 23
  title: Generalized Posteriors in Approximate Bayesian Computation
  type: article-journal
  URL: http://arxiv.org/abs/2011.08644

- id: SolomonConvolutional2015
  accessed:
    - year: 2018
      month: 8
      day: 29
  author:
    - family: Solomon
      given: Justin
    - family: Goes
      given: Fernando
      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
  citation-key: SolomonConvolutional2015
  container-title: ACM Transactions on Graphics
  DOI: 10.1145/2766963
  ISSN: 0730-0301
  issue: '4'
  issued:
    - year: 2015
      month: 7
  page: 66:1–66:11
  title: >-
    Convolutional Wasserstein Distances: Efficient Optimal Transportation on
    Geometric Domains
  type: article-journal
  URL: http://doi.acm.org/10.1145/2766963
  volume: '34'

- id: WangProjected2021
  accessed:
    - year: 2024
      month: 2
      day: 21
  author:
    - family: Wang
      given: Yifei
    - family: Chen
      given: Peng
    - family: Li
      given: Wuchen
  citation-key: WangProjected2021
  DOI: 10.48550/arXiv.2102.06350
  issued:
    - year: 2021
      month: 2
      day: 14
  number: arXiv:2102.06350
  publisher: arXiv
  title: >-
    Projected Wasserstein gradient descent for high-dimensional Bayesian
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- id: WangRiemannian2019
  accessed:
    - year: 2019
      month: 8
      day: 12
  author:
    - family: Wang
      given: Prince Zizhuang
    - family: Wang
      given: William Yang
  citation-key: WangRiemannian2019
  container-title: >-
    Proceedings of the 2019 Conference of the North American Chapter of the
    Association for Computational Linguistics: Human Language Technologies,
    Volume 1 (Long and Short Papers)
  DOI: 10.18653/v1/N19-1025
  event-place: Minneapolis, Minnesota
  event-title: NAACL-HLT 2019
  issued:
    - year: 2019
      month: 6
  page: 284–294
  publisher: Association for Computational Linguistics
  publisher-place: Minneapolis, Minnesota
  title: >-
    Riemannian Normalizing Flow on Variational Wasserstein Autoencoder for Text
    Modeling
  type: paper-conference
  URL: https://www.aclweb.org/anthology/N19-1025

- id: ZhangQuantile2020
  accessed:
    - year: 2020
      month: 12
      day: 1
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    - family: Walder
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    - 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
  type: paper-conference
  URL: http://arxiv.org/abs/1912.10200
...
