@string{AI = {Artificial Intelligence}}
@string{CACM = {Communications of the ACM}}
@string{CSL = {Computer Speech and Language}}
@string{CL = {Computational Linguistics}}
@string{InfCtrl = {Information and Control}}
@string{IT = {IEEE Transactions on information theory}}
@string{JACM = {Journal of the ACM}}
@string{JAIR = {Journal of AI Research}}
@string{JMLR = {Journal of Machine Learning Research}}
@string{ML = {Machine Learning}}
@string{NLE = {Journal of Natural Language Engineering}}
@string{MM = {IEEE Transactions on Multimedia}}
@string{PAMI = {IEEE Transactions on Pattern Analysis and Machine Intelligence}}
@string{SIJAD = {SIAM Journal of Algebraic and Discrete Methods}}
@string{SIJC = {SIAM Journal of Computing}}
@string{TASSP = {IEEE Transactions on Acoustics, speech, and Signal Processing}}
@string{TCS = {Theoretical Computer Science}}
@String{TACL = {Transactions of the Association for Computational Linguistics}}
@String{TASLP = {Transactions on Audio, Speech, and Language Processing}}
@string{AAAI= {Proc. of the National Conference on Artificial Intelligence (AAAI)}}
@string{ANLP = {Proc. of ACL Conference on Applied Natural Language Processing}}
@string{ARPA = {Proc. of the ARPA Workshop on Human Language Technology}}
@string{ACCV = {Proceedings of the Asian Conference on Computer Vision (ACCV)}}
@string{AISTAT = {Proceedings of the International Workshop on Artificial Intelligence and Statistics}}
@string{ALT = {Proc. of the International Workshop on Algorithmic Learning Theory (ALT)}}
@string{COLING = {Proc.  the International Conference on Computational Linguistics (COLING)}}
@string{ACL = {Proc. of the Annual Meeting of the Association Computational Linguistics (ACL)}}
@string{COLT = {Proc. of Conference on Learning Theory (COLT)}}
@string{CoNLL = {Proc. of the Annual Conference on Computational Natural Language Learning (CoNLL)}}
@string{CVPR = {The IEEE Conference on Computer Vision and Pattern Recognition (CVPR)}}
@string{DARPA = {Proc. of the DARPA Workshop on Speech and Natural Language}}
@string{ECML = {Proc. of the European Conference on Machine Learning (ECML)}}
@string{FOCS = {IEEE Symp. of Foundation of Computer Science}}
@string{ECCV = {Proc. of the European Conference on Computer Vision (ECCV)}}
@string{IAAI= {Proc. of the National Conference on Innovative Applications of Artificial Intelligence (IAAI)}}
@string{ICML = {Proc. of the International Conference on Machine Learning (ICML)}}
@string{ICASSP = {Proc. of ICASSP}}
@string{IJCAI = {Proc. of the International Joint Conference on Artificial Intelligence (IJCAI)}}
@string{IJCNLP = {Proc. of the International Joint Conference on Natural Language Processing (IJCNLP)}}
@string{ILP = {Proc. of the International Conference Inductive Logic Programming}}
@string{IPW = {Proc. of the International Parsing Workshop}}
@string{IWPT = {Proc. of the International Workshop of Parsing Technology}}
@string{IT = {IEEE Transactions on Information Theory}}
@string{ISMB = {The International Conference on Intelligent Systems for Molecular Biology}}
@string{KR = {Proc. of the International Conference on the Principles of Knowledge Representation and Reasoning}}
@string{NAACL = {Proc. of the Annual Meeting of the North American Association of Computational Linguistics (NAACL)}}
@string{NeurIPS = {Advances in Neural Information Processing Systems (NeurIPS)}}
@string{SIGIR = {Proc. of International Conference on Research and Development in Information Retrieval, SIGIR}}
@string{SIGDAT = {Proc. of the Conference on Empirical Methods for Natural Language Processing (EMNLP)}}
@string{EMNLP = {Proc. of the Conference on Empirical Methods for Natural Language Processing (EMNLP)}}
@string{STOC = {ACM Symp. of the Theory of Computing}}
@string{TMI = {Proc. of the International Conference on Theoretical and Methodological Issues in Machine Translation}}
@string{UWOED = {Proc. of the Annual Conference of the UW Center for the New OED and Text Research}}
@string{JACM = {Journal of the ACM}}
@string{WWW = {The International World Wide Web Conference}}
@string{CIKM = {Proc. of Conference on Information and Knowledge Management (CIKM)}}
@string{AISTATS = {Proc. of the International Conference on Artificial Intelligence and Statistics (AISTATS)}}
@string{LREC = {Proc. of the International Conference on Language Resources and Evaluation (LREC)}}
@string{ICCV = {Proc. of the International Conference on Computer Vision (ICCV)}}
@string{ICLR = {Proc. of the International Conference on Learning Representation (ICLR)}}
@string{UAI = {Proc. of the Conference on Uncertainty in Artificial Intelligence (UAI)}}

@inproceedings{Goodfellow13,
 author = {Goodfellow, Ian J. and Warde-Farley, David and Mirza, Mehdi and Courville, Aaron and Bengio, Yoshua},
 title = {Maxout Networks},
 booktitle = ICML,
 year = {2013},
 location = {Atlanta, GA, USA},
 pages = {III-1319--III-1327}
} 

@inproceedings{Jarrett09, 
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@inproceedings{yian2015,
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}






 

@inproceedings{SPOS,
  title={Stochastic {P}article-{O}ptimization {S}ampling and the {N}on-{A}symptotic
{C}onvergence {T}heory},
  author={Jianyi Zhang and Ruiyi Zhang and Lawrence Carin and Changyou Chen},
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  year={2020}
}

@inproceedings{Holden18,
  title={Beyond {L}og-concavity: {P}rovable {G}uarantees for {S}ampling {M}ulti-modal {D}istributions using {S}imulated {T}empering {L}angevin {M}onte {C}arlo},
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  year={2018}
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@inproceedings{lin17,
  title={{R}untime {N}eural {P}runing},
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@inproceedings{Liwan13,
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@inproceedings{Simsekli2016,
 author = {\c{S}im\c{s}ekli, Umut and Badeau, Roland and Cemgil, A. Taylan and Richard, Ga\"{e}},
 title = {Stochastic {Q}uasi-{N}ewton {L}angevin {M}onte {C}arlo},
 booktitle = ICML,
 year = {2016},
 location = {New York, NY, USA},
 pages = {642--651},
 numpages = {10},
} 


@inproceedings{Niladri18,
    author = {Niladri Chatterji and Nicolas Flammarion and Yi-An Ma and Peter Bartlett and Michael Jordan},
    title = {On the {T}heory of {V}ariance {R}eduction for {S}tochastic {G}radient {M}onte {C}arlo},
    booktitle = ICML,
    location = {Stockholm, Sweden},
    year = {2018},
}




@inproceedings{Simsekli2017,
 author = {\c{S}im\c{s}ekli, Umut},
 title = {Fractional {L}angevin {M}onte {C}arlo: {E}xploring L\'{e}vy {D}riven {S}tochastic {D}ifferential {E}quations for {M}arkov {C}hain {M}onte {C}arlo
},
 booktitle = ICML,
 year = {2017},
 location = {Sydney, Australia},
 numpages = {10},
} 

@inproceedings{i2SB_guanhong,
 author = {Guan-Horng Liu and Arash Vahdat and De-An Huang and Evangelos A. Theodorou and Weili Nie and Anima Anandkumar},
 title = {{I²SB: Image-to-Image Schrödinger Bridge}},
 booktitle = ICML,
 year = {2023}
} 



@article{Simsekli2019a,
   author = {\c{S}im\c{s}ekli, Umut and Mert G\"{u}rb\"{u}zbalaban and Thanh Huy Nguyen and Ga\"{e}l Richard and Levent Sagun},
    title = {On the {H}eavy-{T}ailed {T}heory of {S}tochastic {G}radient {D}escent for {D}eep {N}eural {N}etworks},
  journal = {ArXiv e-prints},
archivePrefix = "arXiv",
   eprint = {1901.06053},
 primaryClass = "stat.ML",
 keywords = {Statistics - Machine Learning},
     year = {2019},
}

@article{ode_is_fast,
   author = {Sitan Chen and Sinho Chewi and Holden Lee and Yuanzhi Li and Jianfeng Lu and Adil Salim},
    title = {{The Probability Flow ODE is Provably Fast}},
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 keywords = {Statistics - Machine Learning},
     year = {2023},
}

@inproceedings{Simsekli2019b,
 author = {\c{S}im\c{s}ekli, Umut and Levent Sagun and Mert G\"{u}rb\"{u}zbalaban},
 title = {A {T}ail-{I}ndex {A}nalysis of {S}tochastic {G}radient {N}oise in {D}eep {N}eural {N}etworks},
 booktitle = ICML,
 year = {2019},
 location = {Long Beach, CA, USA},
 numpages = {10},
} 







@InProceedings{ye18,
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  booktitle = 	 ICML,
  pages = 	 {5620--5629},
  year = 	 {2018},
  volume = 	 {80},
  month = 	 {10--15 Jul},
}

@inproceedings{Ahn12,
  author = {Sungjin Ahn and Anoop Korattikara and Max Welling},
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}


@article{Amodei16,
   author = {Dario Amodei and Chris Olah and Jacob Steinhardt and Paul Christiano and John Schulman and Dan Man{\'e}},
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  journal = {ArXiv e-prints},
	archivePrefix = "arXiv",
   eprint = {1606.06565},
 primaryClass = "cs.AI",
 keywords = {Computer Science - Artificial Intelligence, Computer Science - Learning},
     year = {2016},
   adsurl = {http://adsabs.harvard.edu/abs/2016arXiv160606565A},
  adsnote = {Provided by the SAO/NASA Astrophysics Data System}
}

@inproceedings{Kendall17,
  author    = {Alex Kendall and Yarin Gal},
  title     = {What Uncertainties Do We Need in {B}ayesian Deep Learning for Computer Vision?},
  booktitle = NeurIPS,
  month = dec,
  year      = {2017}
}

@inproceedings{zimingzhang17,
  author    = {Ziming Zhang and Matthew Brand},
  title     = {Convergent block coordinate descent
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  booktitle = NeurIPS,
  month = dec,
  year      = {2017}
}

@inproceedings{Yarin16b,
  author    = {Yarin Gal and Zoubin Ghahramani},
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  month = dec,
  year      = {2016}
}

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@article{andrieu05,
 author = {Christophe Andrieu and \'{E}ric Moulines and Pierre Priouret},
 journal = {SIAM J. Control Optim.},
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 pages = {283–312},
 title = {Stability of {S}tochastic {A}pproximation under {V}erifiable {C}onditions},
 volume = {44},
 year = {2005}
}

%%%%%%%%%%%%%%%%% Difussion Model / Schrodinger Bridge



@inproceedings{CSDI,
  author    = {Yusuke Tashiro and Jiaming Song and Yang Song and Stefano Ermon},
  title     = {{CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation}},
  booktitle = NeurIPS,
  year      = {2021}
}



@inproceedings{Conditional_DSB,
  author    = {Yuyang Shi and De Bortoli, Valentin and George Deligiannidis and Arnaud Doucet},
  title     = {{Conditional Simulation Using Diffusion Schr\"{o}dinger Bridges}},
  booktitle = UAI,
  year      = {2022}
}


















% Kenneth Caluya and Abhishek Halder. Wasserstein proximal algorithms for the schrödinger bridge
% problem: Density control with nonlinear drift. IEEE Transactions on Automatic Control, 2021.



@article{Paul12,
 author = {Paul Dupuis and Yufei Liu and Nuria Plattner and J. D. Doll},
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@article{Neal01,
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@inproceedings{Aitchison2021,
 author = {Laurence Aitchison},
 title = {A {S}tatistical {T}heory of {C}old {P}osteriors in {D}eep {N}eural {N}etworks},
 booktitle = ICLR,
 year = {2021}
}



@article{andrieu06,
 author = {Christophe Andrieu and \'{E}ric Moulines},
 journal = {The Annals of Applied Probability},
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@article{Pardoux01,
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@article{PhysRevLett85,
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  pages   = {1-48},
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@article{Geyer91,
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@article{Kirkpatrick83optimizationby,
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 author = {Herbert Robbins and Sutton Monro},
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@inproceedings{Blundell15,
 author = {Blundell, Charles and Cornebise, Julien and Kavukcuoglu, Koray and Wierstra, Daan},
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 booktitle = ICML,
 year = {2015},
 location = {Lille, France},
 pages = {1613--1622}
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 author = {Isma{\"e}l Castillo and Aad van der Vaart},
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 year = {2012}
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@article{Andrieu09,
 author = {Christophe Andrieu and Gareth O. Roberts},
 journal = {The Annals of Statistics},
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@article{Liang10,
 author = {Faming Liang},
 journal = {The Annals of Statistics},
 pages = {2823–2856},
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 year = {2010}
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 author = {Chen, Changyou and Ding, Nan and Carin, Lawrence},
 title = {On the {C}onvergence of {S}tochastic {G}radient {MCMC} {A}lgorithms with {H}igh-order {I}ntegrators},
 booktitle = NeurIPS,
 year = {2015},
 location = {Montreal, Canada},
 pages = {2278--2286},
 numpages = {9}
} 

@inproceedings{chen16_distributed,
 author = {Chen, Changyou and Ding, Nan and Chunyuan Li and Yizhe Zhang and Lawrence Carin},
 title = {Stochastic {G}radient {MCMC} with {S}tale {G}radients},
 booktitle = NeurIPS,
 year = {2016}
} 

@inproceedings{landscape18,
 author = {Hao Li and Zheng Xu and Gavin Taylor and Christoph Studer and Tom Goldstein},
 title = {Visualizing the {L}oss {L}andscape of {N}eural {N}ets},
 booktitle = NeurIPS,
 year = {2018},
 numpages = {9}
} 




@inproceedings{Li16,
 author = {Li, Chunyuan and Chen, Changyou and Carlson, David and Carin, Lawrence},
 title = {Preconditioned {S}tochastic {G}radient {L}angevin {D}ynamics for {D}eep {N}eural {N}etworks},
 booktitle = AAAI,
 year = {2016},
 location = {Phoenix, Arizona},
 pages = {1788--1794},
 numpages = {7}
} 






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booktitle = AISTATS,
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pages= {207--215}
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@inproceedings{Denker90,
 author = {Denker, John S. and LeCun, Yann},
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 author = {Nahum Shimkin},
 title = {Introduction to {S}tochastic
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 year={2011},
} 


@article{Diebolt94,
 author = {Jean Diebolt and Christian P. Robert},
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@inproceedings{Gal16a,
Author = {Yarin Gal and Zoubin Ghahramani},
Title = {{B}ayesian {C}onvolutional {N}eural {N}etworks with {B}ernoulli {A}pproximate {V}ariational {I}nference},
Year = {2016},
booktitle = {ICLR workshop},
}

@inproceedings{wangyi06,
Author = {Yi Wang and Nevin L. Zhang},
Title = {Severity of {L}ocal {M}axima for the {EM} Algorithm: {E}xperiences with {H}ierarchical {L}atent {C}lass {M}odels},
Year = {2006},
booktitle = {the Third European Workshop on Probabilistic Graphical Models},
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@InProceedings{Jose_adam_15,
  title = 	 {Probabilistic {B}ackpropagation for {S}calable {L}earning of {B}ayesian {N}eural {N}etworks},
  author = 	 {Jose Miguel Hernandez-Lobato and Ryan Adams},
  booktitle = ICML,
  pages = 	 {1861--1869},
  year = 	 {2015},
  volume = 	 {37},
}

@inproceedings{Gal16b,
Author = {Yarin Gal and Zoubin Ghahramani},
Title = {Dropout as a {B}ayesian {A}pproximation: {R}epresenting {M}odel {U}ncertainty in {D}eep {L}earning},
booktitle = ICML,
year={2016}
}

@PhdThesis{Gal16c,
  title={Uncertainty in {D}eep {L}earning},
  author={Gal, Yarin},
  year={2016},
  school={University of Cambridge}
}

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@book{Amari85,
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@book{Albert90,
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@book{Meyn09,
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    year = {2009}
}


@book{Goodfellow16,
    title={Deep {L}earning},
    author={Ian Goodfellow and Yoshua Bengio and Aaron Courville},
    publisher={MIT Press},
    year={2016}
}

@book{Protter05,
    author={Philip E. Protter},
    title={{Stochastic Integration and Differential Equations}},
    publisher={Springer},
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}


@book{Gelman13,
author = {Andrew Gelman and John B. Carlin and Hal S. Stern and David B. Dunson and Aki Vehtari and Donald B. Rubin},
title={{B}ayesian {D}ata {A}nalysis, Third Edition},
year={2013},
month=nov,
publisher = {CRC press}
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@book{David04,
author = {David Applebaum},
title={L\'{e}vy {P}rocesses and {S}tochastic {C}alculus},
year={2004},
publisher = {Cambridge University Press}
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@book{Hastie15,
author = {Trevor Hastie and Robert Tibshirani and Martin Wainwright},
title={{S}tatistical learning with sparsity:  The lasso and
generalizations.},
year={2015},
publisher = {CRC press}
}


@book{Resnick02,
author = {Resnick, Sidney I.},
title={Adventures in {S}tochastic {P}rocesses},
year={2002},
publisher = {Springer}
}

@book{Liptser01,
author = {Robert S. Liptser and Albert N. Shiryaev},
title={{Statistics of Random Processes: I. General Theory}},
year={2001},
publisher = {Springer Science \& Business Media}
}

@book{skorohod,
  title={Asymptotic methods in the theory of stochastic differential equations},
  author={Skorokhod, Anatoli{\u\i} Vladimirovich},
  volume={78},
  year={2009},
  publisher={American Mathematical Soc.}
}








@article{doi:10.1198/016214506000001437,
author = {Tilmann Gneiting and Adrian E Raftery},
title = {Strictly Proper Scoring Rules, Prediction, and Estimation},
journal = {Journal of the American Statistical Association},
volume = {102},
number = {477},
pages = {359--378},
year  = {2007},
publisher = {Taylor & Francis},
doi = {10.1198/016214506000001437},

URL = { 
        https://doi.org/10.1198/016214506000001437
    
},
eprint = { 
        https://doi.org/10.1198/016214506000001437
    
}
}


@inproceedings{song2020sliced,
  title={{Sliced Score Matching: A Scalable Approach to Density and Score Estimation}},
  author={Song, Yang and Garg, Sahaj and Shi, Jiaxin and Ermon, Stefano},
  booktitle={Uncertainty in Artificial Intelligence},
  year={2020}
}

@article{song2019generative,
  title={Generative modeling by estimating gradients of the data distribution},
  author={Song, Yang and Ermon, Stefano},
  journal={Advances in Neural Information Processing Systems},
  volume={32},
  year={2019}
}

@article{vahdat2021score,
  title={{Score-based Generative Modeling in Latent Space}},
  author={Vahdat, Arash and Kreis, Karsten and Kautz, Jan},
  journal={Advances in Neural Information Processing Systems},
  volume={34},
  pages={11287--11302},
  year={2021}
}

@article{song2020score,
  title={Score-based generative modeling through stochastic differential equations},
  author={Song, Yang and Sohl-Dickstein, Jascha and Kingma, Diederik P and Kumar, Abhishek and Ermon, Stefano and Poole, Ben},
  journal={arXiv preprint arXiv:2011.13456},
  year={2020}
}

@article{matheson1976scoring,
  title={Scoring rules for continuous probability distributions},
  author={Matheson, James E and Winkler, Robert L},
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}

@article{loshchilov2017decoupled,
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  author={Loshchilov, Ilya and Hutter, Frank},
  journal={arXiv preprint arXiv:1711.05101},
  year={2017}
}

@article{grathwohl2018ffjord,
  title={Ffjord: Free-form continuous dynamics for scalable reversible generative models},
  author={Grathwohl, Will and Chen, Ricky TQ and Bettencourt, Jesse and Sutskever, Ilya and Duvenaud, David},
  journal={arXiv preprint arXiv:1810.01367},
  year={2018}
}

@inproceedings{fortuin2020gp,
  title={Gp-vae: Deep probabilistic time series imputation},
  author={Fortuin, Vincent and Baranchuk, Dmitry and R{\"a}tsch, Gunnar and Mandt, Stephan},
  booktitle={International conference on artificial intelligence and statistics},
  pages={1651--1661},
  year={2020},
  organization={PMLR}
}

@article{bonilla2007multi,
  title={Multi-task Gaussian process prediction},
  author={Bonilla, Edwin V and Chai, Kian and Williams, Christopher},
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  volume={20},
  year={2007}
}

@inproceedings{luo2019e2gan,
  title={E2gan: End-to-end generative adversarial network for multivariate time series imputation},
  author={Luo, Yonghong and Zhang, Ying and Cai, Xiangrui and Yuan, Xiaojie},
  booktitle={Proceedings of the 28th international joint conference on artificial intelligence},
  pages={3094--3100},
  year={2019},
  organization={AAAI Press}
}

@article{fang2020time,
  title={Time Series Data Imputation: A Survey on Deep Learning Approaches},
  author={Fang, Chenguang and Wang, Chen},
  journal={arXiv preprint arXiv:2011.11347},
  year={2020}
}

@article{ng2001discriminative,
  title={On discriminative vs. generative classifiers: A comparison of logistic regression and naive bayes},
  author={Ng, Andrew and Jordan, Michael},
  journal={Advances in neural information processing systems},
  volume={14},
  year={2001}
}

@article{du2022saits,
  title={SAITS: Self-Attention-based Imputation for Time Series},
  author={Du, Wenjie and C{\^o}t{\'e}, David and Liu, Yan},
  journal={arXiv preprint arXiv:2202.08516},
  year={2022}
}

@inproceedings{esser2018variational,
  title={A variational u-net for conditional appearance and shape generation},
  author={Esser, Patrick and Sutter, Ekaterina and Ommer, Bj{\"o}rn},
  booktitle={Proceedings of the IEEE conference on computer vision and pattern recognition (CVPR'18)},
  pages={8857--8866},
  year={2018}
}

@inproceedings{U_Air,
  title={{U-Air: When Urban Air Quality Inference Meets Big Data}},
  author={Yu Zheng and Furui Liu and Hsun-Ping Hsieh},
  booktitle={Proceedings of the 19th SIGKDD conference on Knowledge Discovery and Data Mining (KDD'13)},
  year={2013}
}

@inproceedings{ronneberger2015u,
  title={{U-Net: Convolutional Networks for Biomedical Image Segmentation}},
  author={Ronneberger, Olaf and Fischer, Philipp and Brox, Thomas},
  booktitle={International Conference on Medical image computing and computer-assisted intervention},
  pages={234--241},
  year={2015},
  organization={Springer}
}

@inproceedings{rezende2014stochastic,
  title={Stochastic backpropagation and approximate inference in deep generative models},
  author={Rezende, Danilo Jimenez and Mohamed, Shakir and Wierstra, Daan},
  booktitle={International conference on machine learning},
  pages={1278--1286},
  year={2014},
  organization={PMLR}
}

@inproceedings{reflected_diffusion_model,
  title={{Reflected Diffusion Models}},
  author={Aaron Lou and Stefano Ermon},
  booktitle=ICML,
  year={2023}
}

@inproceedings{rasul2021autoregressive,
  title={{Autoregressive Denoising Diffusion Models for Multivariate Probabilistic Time Series Forecasting}},
  author={Rasul, Kashif and Seward, Calvin and Schuster, Ingmar and Vollgraf, Roland},
  booktitle={International Conference on Machine Learning},
  pages={8857--8868},
  year={2021},
  organization={PMLR}
}


@inproceedings{Sampling_Hamiltonian,
  title={{Sampling with Riemannian Hamiltonian Monte Carlo in a Constrained Space}},
  author={Yunbum Kook and Yin Tat Lee and Ruoqi Shen and Santosh S. Vempala},
  booktitle={NeurIPS},
  year={2022},
}

@inproceedings{Riemannian_score_generative,
  title={{Riemannian Score-Based Generative Modelling}},
  author={De Bortoli, Valentin and \'Emile Mathieu and Michael Hutchinson and James Thornton and Yee Whye Teh and Arnaud Doucet},
  booktitle=NeurIPS,
  year={2022},
}



@article{Penalized_Langevin_Hamiltonian,
  title={{Penalized Langevin and Hamiltonian Monte Carlo Algorithms for Constrained Sampling}},
  author={Mert G\"urb\"uzbalaban and Yuanhan Hu and Lingjiong Zhu},
  journal={arXiv:2212.00570v1},
  year={2022}
}



@article{rasul2020multivariate,
  title={{Multivariate Probabilistic Time Series Forecasting via Conditioned Normalizing Flows}},
  author={Rasul, Kashif and Sheikh, Abdul-Saboor and Schuster, Ingmar and Bergmann, Urs and Vollgraf, Roland},
  journal={arXiv preprint arXiv:2002.06103},
  year={2020}
}

@article{Diffusion_constrained,
  title={{Diffusion Models for Constrained Domains}},
  author={Nic Fishman and Leo Klarner and  De Bortoli, Valentin and Emile Mathieu and Michael Hutchinson},
  journal={ Transactions on Machine Learning Research},
  year={2023}
}


@article{rangapuram2018deep,
  title={{Deep State Space Models for Time Series Forecasting}},
  author={Rangapuram, Syama Sundar and Seeger, Matthias W and Gasthaus, Jan and Stella, Lorenzo and Wang, Yuyang and Januschowski, Tim},
  journal={Advances in neural information processing systems},
  volume={31},
  year={2018}
}

@article{shih2019temporal,
  title={{Temporal Pattern Attention for Multivariate Time Series Forecasting}},
  author={Shih, Shun-Yao and Sun, Fan-Keng and Lee, Hung-yi},
  journal={Machine Learning},
  volume={108},
  number={8},
  pages={1421--1441},
  year={2019},
  publisher={Springer}
}

@article{qin2017dual,
  title={{A Dual-stage Attention-based Recurrent Neural Network for Time Series Prediction}},
  author={Qin, Yao and Song, Dongjin and Chen, Haifeng and Cheng, Wei and Jiang, Guofei and Cottrell, Garrison},
  journal={arXiv preprint arXiv:1704.02971},
  year={2017}
}


@article{che2018recurrent,
  title={{Recurrent Neural Networks for Multivariate Time Series with Missing Values}},
  author={Che, Zhengping and Purushotham, Sanjay and Cho, Kyunghyun and Sontag, David and Liu, Yan},
  journal={Scientific reports},
  volume={8},
  number={1},
  pages={1--12},
  year={2018},
  publisher={Nature Publishing Group}
}

@article{yoon2018,
  title={{Estimating Missing Data in Temporal Data Streams using Multi-Directional Recurrent Neural Networks}},
  author={Yoon, Jinsung and Zame, William R and van der Schaar, Mihaela},
  journal={IEEE Transactions on Biomedical Engineering},
  volume={66},
  number={5},
  pages={1477--1490},
  year={2018},
  publisher={IEEE}
}




@article{multitask_GP,
  title={{Multitask Gaussian processes for Multivariate Physiological Time-Series Analysis}},
  author={D{\"u}richen, Robert and Pimentel, Marco AF and Clifton, Lei and Schweikard, Achim and Clifton, David A},
  journal={IEEE Transactions on Biomedical Engineering},
  volume={62},
  number={1},
  pages={314--322},
  year={2014},
  publisher={IEEE}
}

@article{v_rin,
  title={{Uncertainty-aware Variational-recurrent Imputation Network for Clinical Time Series}},
  author={Mulyadi, Ahmad Wisnu and Jun, Eunji and Suk, Heung-Il},
  journal={IEEE Transactions on Cybernetics},
  year={2021},
  publisher={IEEE}
}



@article{Sitan_22_sampling_is_easy,
  title={{Sampling is as Easy as Learning the Score: Theory for Diffusion Models with Minimal Data Assumptions}},
  author={Sitan Chen and Sinho Chewi and Jerry Li and Yuanzhi Li and Adil Salim and Anru R. Zhang},
  journal={arXiv preprint arXiv:2209.11215v2},
  year={2022}
}

@article{gigli2013log,
  title={{From Log Sobolev to Talagrand: a Quick Proof}},
  author={Gigli, Nicola and Ledoux, Michel},
  journal={Discrete and Continuous Dynamical Systems-Series A},
  pages={dcds--2013},
  year={2013}
}

@article{otto2000generalization,
  title={{Generalization of an Inequality by Talagrand and Links with the Logarithmic Sobolev Inequality}},
  author={Otto, Felix and Villani, C{\'e}dric},
  journal={Journal of Functional Analysis},
  volume={173},
  number={2},
  pages={361--400},
  year={2000},
  publisher={Elsevier}
}

@article{bobkov1999exponential,
  title={{Exponential Integrability and Transportation Cost Related to Logarithmic Sobolev Inequalities}},
  author={Bobkov, Sergej G and G{\"o}tze, Friedrich},
  journal={Journal of Functional Analysis},
  volume={163},
  number={1},
  pages={1--28},
  year={1999},
  publisher={Elsevier}
}

@article{zhang2020non,
  title={{On the Non-asymptotic and Sharp Lower Tail Bounds of Random Variables}},
  author={Zhang, Anru R and Zhou, Yuchen},
  journal={Stat},
  volume={9},
  number={1},
  pages={e314},
  year={2020},
  publisher={Wiley Online Library}
}


@article{kantorovich1958space,
  title={{On a Space of Totally Additive Functions}},
  author={Kantorovich, Leonid Vasilevich and Rubinshtein, SG},
  journal={Vestnik of the St. Petersburg University: Mathematics},
  volume={13},
  number={7},
  pages={52--59},
  year={1958},
  publisher={Allerton Press, Inc.}
}

@article{hu2013kullback,
  title={{Kullback-Leibler Divergence Constrained Distributionally Robust Optimization}},
  author={Hu, Zhaolin and Hong, L Jeff},
  journal={Available at Optimization Online},
  pages={1695--1724},
  year={2013}
}
@article{djellout2004transportation,
  title={{Transportation Cost-information Inequalities and Applications to Random Dynamical Systems and Diffusions}},
  author={Djellout, Hacene and Guillin, Arnaud and Wu, Liming},
  journal={The Annals of Probability},
  volume={32},
  number={3B},
  pages={2702--2732},
  year={2004},
  publisher={Institute of Mathematical Statistics}
}


@article{leonard_14,
  title={{A Survey of the Schr\"{o}dinger Problem and Some of its Connections with Optimal Transport}},
  author={L\'{e}onard, Christian},
  journal={Discrete \& Continuous Dynamical Systems-A},
  volume={34},
  number={4},
  pages={1533–1574},
  year={2014}
}

@article{leonard_01,
  title={{Minimization of Energy Functionals Applied to Some Inverse Problems}},
  author={L\'{e}onard, Christian},
  journal={Applied Mathematics and Optimization volume},
  volume={44},
  pages={273–297},
  year={2001}
}



%%%%%%%%%%%%%%%%% New-added by fang

@article{SBP_max_llk,
  title={{Solving Schr{\"o}dinger Bridges via Maximum Likelihood}},
  author={Vargas, Francisco and Thodoroff, Pierre and Lamacraft, Austen and Lawrence, Neil},
  journal={Entropy},
  volume={23},
  number={9},
  pages={1134},
  year={2021},
  publisher={MDPI}
}


@article{ho2022classifier,
  title={{Classifier-free Diffusion Guidance}},
  author={Ho, Jonathan and Salimans, Tim},
  journal={arXiv preprint arXiv:2207.12598},
  year={2022}
}

@article{reflected_non_convex,
  title={{Convergence Error Analysis of Reflected Gradient Langevin Dynamics for Globally Optimizing Non-Convex Constrained Problems}},
  author={Kanji Sato and Akiko Takeda and Reiichiro Kawai and  Taiji Suzuki},
  journal={arXiv:2203.10215},
  year={2022}
}

@inproceedings{lu2022conditional,
  title={{Conditional Diffusion Probabilistic Model for Speech Enhancement}},
  author={Lu, Yen-Ju and Wang, Zhong-Qiu and Watanabe, Shinji and Richard, Alexander and Yu, Cheng and Tsao, Yu},
  booktitle={ICASSP 2022-2022 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)},
  pages={7402--7406},
  year={2022},
  organization={IEEE}
}


@inproceedings{phy_2012,
  title={{Predicting Inhospital Mortality of ICU patients: The Physionet/Computing in Cardiology Challenge 2012}},
  author={Ikaro Silva and George Moody and Daniel J Scott and Leo A Celi and Roger G Mark},
  booktitle={Computing in Cardiology},
  pages={245–248},
  year={2012},
  organization={IEEE}
}

%%%%%%%%%%%%%%%%% Difussion Model / Schrodinger Bridge

@inproceedings{khrulkov2022understanding,
  title={{Understanding DDPM Latent Codes through Optimal Transport}},
  author={Khrulkov, Valentin and Oseledets, Ivan},
  booktitle=ICLR,
  year={2023}
}


@inproceedings{SB_closed_form,
  title={{Recovering Stochastic Dynamics via Gaussian Schr\"{o}dinger Bridges}},
  author={Bunne, Charlotte and Hsieh, Ya-Ping and Cuturi, marco and Krause, Andreas},
  booktitle=AISTAT,
  year={2023}
}

@inproceedings{riemannian_flow_matching_general_geo,
  title={{Riemannian Flow Matching on General Geometries}},
  author={Ricky T. Q. Chen and Yaron Lipman},
  booktitle={arXiv preprint arXiv:2302.03660},
  year={2023}
}

@inproceedings{momentum_SB,
  title={{Deep Momentum Multi-Marginal Schr\"{o}dinger Bridge}},
  author={Tianrong Chen and Guan-Horng Liu and Molei Tao and Evangelos A. Theodorou},
  booktitle={arXiv:2303.01751v1},
  year={2023}
}

@inproceedings{align_SB,
  title={{Aligned Diffusion Schr\"{o}dinger Bridges}},
  author={Vignesh Ram Somnath and Matteo Pariset and Ya-Ping Hsieh and Maria Rodriguez Martinez and Andreas Krause and Charlotte Bunne},
  booktitle={arXiv:2302.11419},
  year={2023}
}


@inproceedings{transport_support,
  title={{Transport with Support: Data-Conditional Diffusion Bridges}},
  author={Ella Tamir and Martin Trapp and Arno Solin},
  booktitle={	arXiv:2301.13636},
  year={2023}
}


@inproceedings{Inversion_by_Direct_Iteration,
  title={{Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration}},
  author={Mauricio Delbracio and Peyman Milanfar},
  booktitle={arXiv:2303.11435},
  year={2023}
}

@inproceedings{diffusion_bridge_qiang,
  title={{Learning Diffusion Bridges on Constrained Domains}},
  author={Xingchao Liu and Lemeng Wu and Mao Ye and Qiang Liu},
  booktitle=ICLR,
  year={2023}
}


@inproceedings{Iterative_blending,
  title={{Iterative $\alpha$-(de)Blending: Learning a Deterministic Mapping Between Arbitrary Densities}},
  author={Eric Heitz and Laurent Belcour and Thomas Chambon},
  booktitle={https://openreview.net/forum?id=s7gnrEtWSm},
  year={2023}
}

@inproceedings{Progressive_distillation,
  title={{Progressive Distillation for Fast Sampling of Diffusion Models}},
  author={Tim Salimans and Jonathan Ho},
  booktitle=ICLR,
  year={2022}
}

@inproceedings{Consistency_models,
  title={{Consistency Models}},
  author={Yang Song and Prafulla Dhariwal and Mark Chen and Ilya Sutskever},
  booktitle=ICML,
  year={2023}
}

@inproceedings{Distillation_1st_work,
  title={{Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed}},
  author={Eric Luhman and Troy Luhman},
  booktitle={arXiv preprint arXiv:2101.02388},
  year={2021}
}

@inproceedings{Diffusion_bridge,
  title={{Simulating Diffusion Bridges with Score Matching}},
  author={Jeremy Heng and Valentin De Bortoli and Arnaud Doucet and James Thornton},
  booktitle={arXiv:2111.07243},
  year={2022}
}

@inproceedings{DSNO_distillation,
  title={{Fast Sampling of Diffusion Models via Operator Learning}},
  author={Hongkai Zheng and Weilie Nie and Arash Vahdat and Kamyar Azizzadenesheli and Anima Anandkumar},
  booktitle={arXiv:2211.13449v2},
  year={2023}
}

@inproceedings{ ,
  title={{ }},
  author={ },
  booktitle={},
  year={2023}
}



%%% starting module =========== some added by Wei
@inproceedings{STMVL,
  author    = {Xiuwen Yi and Yu Zheng and Junbo Zhang and Tianrui Li},
  title     = {{ST-MVL: Filling Missing Values in Geo-sensory Time Series Data}},
  booktitle = IJCAI,
  year      = {2016}
}

@inproceedings{BRITS,
  author    = {Wei Cao and Dong Wang and Jian Li and Hao Zhou and Lei Li and Yitan Li},
  title     = {{BRITS: Bidirectional Recurrent Imputation for Time Series}},
  booktitle = NeurIPS,
  year      = {2018}
}

@inproceedings{TSI_GAN,
  author    = {Yonghong Luo and Xiangrui Cai and Ying Zhang and Jun Xu and Xiaojie Yuan},
  title     = {{Multivariate Time Series Imputation with Generative Adversarial Networks}},
  booktitle = NeurIPS,
  year      = {2018}
}


@inproceedings{Mirror_Diffusion,
  author    = {Guan-Horng Liu and Tianrong Chen and Evangelos A. Theodorou and Molei Tao},
  title     = {{Mirror Diffusion Models for Constrained and Watermarked Generation}},
  booktitle = NeurIPS,
  year      = {2023}
}

@inproceedings{GP_VAE,
  author    = {Vincent Fortuin and Dmitry Baranchuk and Gunnar R\"{a}tsch and Stephan Mandt},
  title     = {{GP-VAE: Deep Probabilistic Time Series Imputation}},
  booktitle =  AISTATS,
  year      = {2020}
}

@inproceedings{attention_ts,
  author    = {Satya Narayan Shukla and Benjamin M Marlin},
  title     = {{Multi-time Attention Networks for Irregularly Sampled Time Series}},
  booktitle = ICLR,
  year      = {2021}
}

@inproceedings{Ladder_VAE,
  author    = {Casper Kaae S{\o}nderby and  Tapani Raiko and Lars Maal\o e and S{\o}ren Kaae S{\o}nderby and Ole Winther},
  title     = {{Ladder Variational Autoencoders}},
  booktitle = {Neural Information Processing Systems (NIPS)},
  year      = {2016}
}

@inproceedings{EMBs,
  author    = {Salakhutdinov, Ruslan and Hinton, Geoffrey},
  title     = {{Deep Boltzmann Machines}},
  booktitle = AISTAT,
  year      = {2009}
}
%%% ending module =========== some added by Wei



@inproceedings{Aitchison2021,
 author = {Laurence Aitchison},
 title = {A {S}tatistical {T}heory of {C}old {P}osteriors in {D}eep {N}eural {N}etworks},
 booktitle = ICLR,
 year = {2021}
}



@article{andrieu06,
 author = {Christophe Andrieu and \'{E}ric Moulines},
 journal = {The Annals of Applied Probability},
 number = {3},
 pages = {1462–1505},
 title = {On the {E}rgodicity {P}roperties of {S}ome {A}daptive {MCMC} {A}lgorithms},
 volume = {16},
 year = {2006}
}

@article{Pardoux01,
 author = {E. Pardoux and A. Yu. Veretennikov},
 journal = {The Annals of Probability},
 number = {3},
 pages = {1061–1085},
 title = {On the {P}oisson {E}quation and {D}iffusion {A}pproximation {I}.},
 volume = {29},
 year = {2001}
}

@article{Harrison_1987,
 author = {J Michael Harrison and Ruth J Williams},
 title = {{Multidimensional Reflected Brownian Motions Having Exponential Stationary Distributions}},
 number = {15:1},
 pages = {115–137},
 journal = {The Annals of Probability},
 year = {1987}
}

@article{Eric,
 author = {Eric Vanden-Eijnden},
 journal = {Slides},
 title = {Introduction to {R}egular {P}erturbation {T}heory},
 url={https://cims.nyu.edu/~eve2/reg_pert.pdf},
  year = {2001}
}

@article{Perturbation2,
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