---
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      day: 2
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    - family: Peherstorfer
      given: Benjamin
  citation-key: AlsupMultilevel2022
  container-title: >-
    Proceedings of the 2nd Mathematical and Scientific Machine Learning
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  DOI: 10.48550/arXiv.2104.01945
  event-title: Mathematical and Scientific Machine Learning
  ISSN: 2640-3498
  issued:
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      month: 4
      day: 30
  language: en
  page: 93-117
  publisher: PMLR
  title: >-
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- id: AmbrogioniWasserstein2018
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  citation-key: AmbrogioniWasserstein2018
  collection-title: NIPS'18
  container-title: >-
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  issued:
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- id: AnastasiouStein2023
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  publisher: Institute of Mathematical Statistics
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- id: ChenProjected2020
  accessed:
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      month: 12
      day: 21
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      month: 2
      day: 9
  number: arXiv:1901.08659
  publisher: arXiv
  title: >-
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- id: ChuEquivalence2022
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      month: 11
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      month: 6
      day: 14
  language: en
  page: '5'
  title: >-
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- id: ChwialkowskiKernel2016
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      day: 30
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  citation-key: ChwialkowskiKernel2016
  collection-title: ICML'16
  container-title: >-
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- id: DetommasoStein2018
  accessed:
    - year: 2022
      month: 10
      day: 12
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      given: Gianluca
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    - family: Spantini
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    - family: Scheichl
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  citation-key: DetommasoStein2018
  collection-title: NIPS'18
  container-title: >-
    Proceedings of the 32nd International Conference on Neural Information
    Processing Systems
  DOI: 10.48550/arXiv.1806.03085
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      month: 12
      day: 3
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  publisher: Curran Associates Inc.
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  title: A Stein variational Newton method
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- id: DetommasoStein2019
  accessed:
    - year: 2022
      month: 4
      day: 6
  author:
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      given: Gianluca
    - family: Hoitzing
      given: Hanne
    - family: Cui
      given: Tiangang
    - family: Alamir
      given: Ardavan
  citation-key: DetommasoStein2019
  container-title: arXiv:1901.07987 [cs, stat]
  issued:
    - year: 2019
      month: 5
      day: 25
  title: >-
    Stein Variational Online Changepoint Detection with Applications to Hawkes
    Processes and Neural Networks
  type: article-journal
  URL: http://arxiv.org/abs/1901.07987

- id: FengLearning2017
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    - year: 2023
      month: 1
      day: 6
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      given: Yihao
    - family: Wang
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    - family: Liu
      given: Qiang
  citation-key: FengLearning2017
  container-title: UAI 2017
  DOI: 10.48550/arXiv.1707.06626
  issued:
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      month: 10
      day: 30
  publisher: arXiv
  title: Learning to draw samples with amortized Stein variational gradient descent
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- id: GongQuantile2019
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
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      given: Chengyue
    - family: Peng
      given: Jian
    - family: Liu
      given: Qiang
  citation-key: GongQuantile2019
  container-title: Proceedings of the 36th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2019
      month: 5
      day: 24
  language: en
  page: 2347-2356
  publisher: PMLR
  title: Quantile Stein Variational Gradient Descent for Batch Bayesian Optimization
  type: paper-conference
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- id: GorhamMeasuring2015
  accessed:
    - year: 2024
      month: 3
      day: 5
  author:
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      given: Jackson
    - family: Mackey
      given: Lester
  citation-key: GorhamMeasuring2015
  collection-title: NIPS'15
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    Processing Systems - Volume 1
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      month: 12
      day: 7
  page: 226–234
  publisher: MIT Press
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  title: Measuring sample quality with Stein's method
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- id: GorhamStochastic2020
  accessed:
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      month: 3
      day: 30
  author:
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      given: Jackson
    - family: Raj
      given: Anant
    - family: Mackey
      given: Lester
  citation-key: GorhamStochastic2020
  container-title: arXiv:2007.02857 [cs, math, stat]
  issued:
    - year: 2020
      month: 10
      day: 22
  title: Stochastic Stein Discrepancies
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- id: HanStein2018
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
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      given: Jun
    - family: Liu
      given: Qiang
  citation-key: HanStein2018
  container-title: Proceedings of the 35th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2018
      month: 7
      day: 3
  language: en
  page: 1900-1908
  publisher: PMLR
  title: Stein Variational Gradient Descent Without Gradient
  type: paper-conference
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- id: HugginsScalable2018
  accessed:
    - year: 2019
      month: 1
      day: 18
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      given: Jonathan H.
    - family: Campbell
      given: Trevor
    - family: Kasprzak
      given: Mikołaj
    - family: Broderick
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  citation-key: HugginsScalable2018
  container-title: arXiv:1806.10234 [cs, stat]
  issued:
    - year: 2018
      month: 6
      day: 26
  title: >-
    Scalable Gaussian Process Inference with Finite-data Mean and Variance
    Guarantees
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  URL: http://arxiv.org/abs/1806.10234

- id: LeyStein2017
  accessed:
    - year: 2021
      month: 5
      day: 11
  author:
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      given: Christophe
    - family: Reinert
      given: Gesine
    - family: Swan
      given: Yvik
  citation-key: LeyStein2017
  container-title: Probability Surveys
  DOI: 10.1214/16-PS278
  ISSN: 1549-5787, 1549-5787
  issue: none
  issued:
    - year: 2017
      month: 1
  page: 1-52
  publisher: Institute of Mathematical Statistics and Bernoulli Society
  title: Stein’s method for comparison of univariate distributions
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  volume: '14'

- id: LiStochastic2020
  accessed:
    - year: 2024
      month: 3
      day: 8
  author:
    - family: Li
      given: Lei
    - family: Li
      given: Yingzhou
    - family: Liu
      given: Jian-Guo
    - family: Liu
      given: Zibu
    - family: Lu
      given: Jianfeng
  citation-key: LiStochastic2020
  container-title: Communications in Applied Mathematics and Computational Science
  container-title-short: Commun. Appl. Math. Comput. Sci.
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  ISSN: 2157-5452, 1559-3940
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  issued:
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      month: 6
      day: 3
  language: en
  page: 37-63
  title: >-
    A stochastic version of Stein variational gradient descent for efficient
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- id: LiuGrassmann2022
  accessed:
    - year: 2022
      month: 11
      day: 2
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      given: Xing
    - family: Zhu
      given: Harrison
    - family: Ton
      given: Jean-Francois
    - family: Wynne
      given: George
    - family: Duncan
      given: Andrew
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  container-title: >-
    Proceedings of The 25th International Conference on Artificial Intelligence
    and Statistics
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  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
    - year: 2022
      month: 5
      day: 3
  language: en
  page: 2002-2021
  publisher: PMLR
  title: Grassmann Stein Variational Gradient Descent
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  URL: https://proceedings.mlr.press/v151/liu22a.html

- id: LiuKernelized2016
  author:
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      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
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  URL: http://arxiv.org/abs/1602.03253

- id: LiuRiemannian2018
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Liu
      given: Chang
    - family: Zhu
      given: Jun
  citation-key: LiuRiemannian2018
  container-title: Proceedings of the AAAI Conference on Artificial Intelligence
  DOI: 10.1609/aaai.v32i1.11810
  ISSN: 2374-3468
  issue: '1'
  issued:
    - year: 2018
      month: 4
      day: 29
  language: en
  number: '1'
  title: Riemannian Stein Variational Gradient Descent for Bayesian Inference
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  URL: https://ojs.aaai.org/index.php/AAAI/article/view/11810
  volume: '32'

- id: LiuShort2016
  author:
    - family: Liu
      given: Qiang
  citation-key: LiuShort2016
  issued:
    - year: 2016
  language: en
  title: A Short Introduction to Kernelized Stein Discrepancy
  type: article-journal
  URL: http://www.cs.utexas.edu/~lqiang/PDF/ksd_short.pdf

- id: LiuStein2016
  author:
    - family: Liu
      given: Qiang
  citation-key: LiuStein2016
  issued:
    - year: 2016
  language: en
  page: '6'
  title: 'Stein Variational Gradient Descent: Theory and Applications'
  type: article-journal
  URL: http://approximateinference.org/accepted/Liu2016.pdf

- id: LiuStein2017
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Liu
      given: Qiang
  citation-key: LiuStein2017
  DOI: 10.48550/arXiv.1704.07520
  issued:
    - year: 2017
      month: 11
      day: 14
  number: arXiv:1704.07520
  publisher: arXiv
  title: Stein Variational Gradient Descent as Gradient Flow
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  URL: http://arxiv.org/abs/1704.07520

- id: LiuStein2018
  accessed:
    - year: 2022
      month: 11
      day: 1
  author:
    - family: Liu
      given: Qiang
    - family: Wang
      given: Dilin
  citation-key: LiuStein2018
  collection-title: NIPS'18
  container-title: >-
    Proceedings of the 32nd International Conference on Neural Information
    Processing Systems
  DOI: 10.48550/arXiv.1810.11693
  event-place: Red Hook, NY, USA
  issued:
    - year: 2018
      month: 12
      day: 3
  page: 8868–8877
  publisher: Curran Associates Inc.
  publisher-place: Red Hook, NY, USA
  title: Stein variational gradient descent as moment matching
  type: paper-conference
  URL: http://arxiv.org/abs/1810.11693
  volume: '31'

- id: LiuStein2019
  accessed:
    - year: 2019
      month: 11
      day: 11
  author:
    - family: Liu
      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: PielokApproximate2023
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    - year: 2023
      month: 5
      day: 25
  author:
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      given: Tobias
    - family: Bischl
      given: Bernd
    - family: Rügamer
      given: David
  citation-key: PielokApproximate2023
  event-title: The Eleventh International Conference on Learning Representations
  issued:
    - year: 2023
      month: 2
      day: 1
  language: en
  title: >-
    Approximate Bayesian Inference with Stein Functional Variational Gradient
    Descent
  type: paper-conference
  URL: https://openreview.net/forum?id=a2-aoqmeYM4

- id: PulidoKernel2019
  accessed:
    - year: 2022
      month: 12
      day: 21
  author:
    - family: Pulido
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    - family: Van Leeuwen
      given: Peter Jan
    - family: Posselt
      given: Derek J.
  citation-key: PulidoKernel2019
  container-title: >-
    Computational Science – ICCS 2019. ICCS 2019. Lecture Notes in Computer
    Science
  DOI: 10.1007/978-3-030-22747-0_11
  editor:
    - family: Rodrigues
      given: Joao M. F.
    - family: Cardoso
      given: Pedro J. S.
    - family: Monteiro
      given: Janio
    - family: Lam
      given: Roberto
    - family: Krzhizhanovskaya
      given: Valeria V.
    - family: Lees
      given: Michael H.
    - family: Dongarra
      given: Jack J.
    - family: Sloot
      given: Peter M. A.
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  event-title: ICCS 2019
  ISBN: 978-3-030-22746-3
  ISSN: 0302-9743
  issue: '11539'
  issued:
    - year: 2019
      month: 6
  language: en
  number: '11539'
  page: 141-155
  publisher: Springer
  publisher-place: Faro, Portugal
  title: >-
    Kernel embedded nonlinear observational mappings in the variational mapping
    particle filter
  type: paper-conference
  URL: http://arxiv.org/abs/1901.10426

- id: PulidoSequential2019
  accessed:
    - year: 2022
      month: 12
      day: 21
  author:
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      given: Manuel
    - family: Leeuwen
      given: Peter Jan
      non-dropping-particle: van
  citation-key: PulidoSequential2019
  container-title: Journal of Computational Physics
  container-title-short: Journal of Computational Physics
  DOI: 10.1016/j.jcp.2019.06.060
  ISSN: 0021-9991
  issued:
    - year: 2019
      month: 11
      day: 1
  language: en
  page: 400-415
  title: >-
    Sequential Monte Carlo with kernel embedded mappings: The mapping particle
    filter
  type: article-journal
  URL: http://arxiv.org/abs/1805.11380
  volume: '396'

- id: StordalPKernel2021
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Stordal
      given: Andreas S.
    - family: Moraes
      given: Rafael J.
    - family: Raanes
      given: Patrick N.
    - family: Evensen
      given: Geir
  citation-key: StordalPKernel2021
  container-title: Mathematical Geosciences
  container-title-short: Math Geosci
  DOI: 10.1007/s11004-021-09937-x
  ISSN: 1874-8953
  issue: '3'
  issued:
    - year: 2021
      month: 4
      day: 1
  language: en
  page: 375-393
  title: >-
    p-Kernel Stein Variational Gradient Descent for Data Assimilation and
    History Matching
  type: article-journal
  volume: '53'

- id: TamangEnsemble2021
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Tamang
      given: Sagar K.
    - family: Ebtehaj
      given: Ardeshir
    - family: Leeuwen
      given: Peter J.
      non-dropping-particle: van
    - family: Zou
      given: Dongmian
    - family: Lerman
      given: Gilad
  citation-key: TamangEnsemble2021
  container-title: Nonlinear Processes in Geophysics
  container-title-short: Nonlin. Processes Geophys.
  DOI: 10.5194/npg-28-295-2021
  ISSN: 1607-7946
  issue: '3'
  issued:
    - year: 2021
      month: 7
      day: 6
  language: en
  page: 295-309
  title: Ensemble Riemannian data assimilation over the Wasserstein space
  type: article-journal
  URL: https://npg.copernicus.org/articles/28/295/2021/
  volume: '28'

- id: WangFunction2018
  accessed:
    - year: 2023
      month: 5
      day: 25
  author:
    - family: Wang
      given: Ziyu
    - family: Ren
      given: Tongzheng
    - family: Zhu
      given: Jun
    - family: Zhang
      given: Bo
  citation-key: WangFunction2018
  event-title: International Conference on Learning Representations
  issued:
    - year: 2018
      month: 12
      day: 21
  language: en
  title: Function Space Particle Optimization for Bayesian Neural Networks
  type: paper-conference
  URL: https://openreview.net/forum?id=BkgtDsCcKQ

- id: WangNonlinear2019
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Wang
      given: Dilin
    - family: Liu
      given: Qiang
  citation-key: WangNonlinear2019
  container-title: Proceedings of the 36th International Conference on Machine Learning
  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
  issued:
    - year: 2019
      month: 5
      day: 24
  language: en
  page: 6576-6585
  publisher: PMLR
  title: >-
    Nonlinear Stein Variational Gradient Descent for Learning Diversified
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  URL: https://proceedings.mlr.press/v97/wang19h.html

- id: WangStein2018
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
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    - family: Zeng
      given: Zhe
    - family: Liu
      given: Qiang
  citation-key: WangStein2018
  issued:
    - year: 2018
      month: 6
      day: 7
  language: en
  number: arXiv:1711.07168
  publisher: arXiv
  title: Stein Variational Message Passing for Continuous Graphical Models
  type: article
  URL: http://arxiv.org/abs/1711.07168

- id: WangStein2019
  accessed:
    - year: 2022
      month: 11
      day: 1
  author:
    - family: Wang
      given: Dilin
    - family: Tang
      given: Ziang
    - family: Bajaj
      given: Chandrajit
    - family: Liu
      given: Qiang
  citation-key: WangStein2019
  container-title: >-
    Proceedings of the 33rd International Conference on Neural Information
    Processing Systems
  DOI: 10.48550/arXiv.1910.12794
  event-place: Red Hook, NY, USA
  issued:
    - year: 2019
      month: 12
      day: 8
  page: 7836–7846
  PMCID: PMC6923147
  PMID: '31857781'
  publisher: Curran Associates Inc.
  publisher-place: Red Hook, NY, USA
  title: Stein variational gradient descent with matrix-valued kernels
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- id: WenAffinemapping2022
  accessed:
    - year: 2022
      month: 11
      day: 2
  author:
    - family: Wen
      given: Linjie
    - family: Li
      given: Jinglai
  citation-key: WenAffinemapping2022
  container-title: Statistics and Computing
  container-title-short: Stat Comput
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  ISSN: 1573-1375
  issue: '6'
  issued:
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      month: 10
      day: 19
  language: en
  page: '97'
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- id: XuInterpretable2021
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      month: 3
      day: 30
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    - family: Matsuda
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  citation-key: XuInterpretable2021
  container-title: arXiv:2103.00895 [stat]
  issued:
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      month: 3
      day: 1
  title: Interpretable Stein Goodness-of-fit Tests on Riemannian Manifolds
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  URL: http://arxiv.org/abs/2103.00895

- id: ZhangStochastic2020
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  author:
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    - family: Carin
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    - family: Chen
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  citation-key: ZhangStochastic2020
  container-title: International Conference on Artificial Intelligence and Statistics
  event-title: International Conference on Artificial Intelligence and Statistics
  ISSN: 2640-3498
  issued:
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      month: 8
      day: 26
    - year: 2020
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      day: 28
  language: en
  page: 1877-1887
  publisher: PMLR
  title: >-
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- id: ZhaoStein2023
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  citation-key: ZhaoStein2023
  container-title: Information Sciences
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  ISSN: 0020-0255
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  title: Stein variational gradient descent with learned direction
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  volume: '637'

- id: ZhouAugmented2023
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      day: 5
  author:
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  citation-key: ZhouAugmented2023
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      month: 5
      day: 17
  number: arXiv:2305.10636
  publisher: arXiv
  title: Augmented Message Passing Stein Variational Gradient Descent
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- id: ZhuoMessage2018
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    - family: Chen
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    - family: Zhang
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  event-title: International Conference on Machine Learning
  ISSN: 2640-3498
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  language: en
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  publisher: PMLR
  title: Message Passing Stein Variational Gradient Descent
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...
