@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, 
author={K. Jarrett and K. Kavukcuoglu and M. Ranzato and Y. LeCun}, 
booktitle=ICCV, 
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year={2009},
pages={2146-2153},
month=sep
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@inproceedings{paszke2017,
  title={Automatic differentiation in {P}y{T}orch},
  author={Paszke, Adam and Gross, Sam and Chintala, Soumith and Chanan, Gregory and Yang, Edward and DeVito, Zachary and Lin, Zeming and Desmaison, Alban and Antiga, Luca and Lerer, Adam},
  booktitle={NeurIPS Autodiff Workshop},
  year={2017}
}

@inproceedings{yian2015,
  title={A {C}omplete {R}ecipe for {S}tochastic {G}radient {MCMC}},
  author={Yi-An Ma and Tianqi Chen and Emily B. Fox},
  booktitle=NeurIPS,
  year={2015}
}


@inproceedings{Chen_divergence_free,
  title={{Neural Conservation Laws: A Divergence-Free Perspective}},
  author={Jack Richter-Powell and Yaron Lipman and Ricky T. Q. Chen},
  booktitle=NeurIPS,
  year={2022}
}

@inproceedings{FFJORD,
  title={{FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models}},
  author={Will Grathwohl and Ricky T. Q. Chen and Jesse Bettencourt and Ilya Sutskever and David Duvenaud},
  booktitle=ICLR,
  year={2019}
}

@inproceedings{neural_ode,
  title={{Neural Ordinary Differential Equations}},
  author={Ricky T. Q. Chen and Yulia Rubanova and Jesse Bettencourt and David Duvenaud},
  booktitle= NeurIPS,
  year={2018}
}

@inproceedings{control_neural_ode,
  title={{Neural Controlled Differential Equations for Irregular Time Series}},
  author={Patrick Kidger and James Morrill and James Foster and Terry Lyons},
  booktitle= NeurIPS,
  year={2020}
}

@inproceedings{CTFP,
  title={{Modeling Continuous Stochastic Processes with Dynamic Normalizing Flows}},
  author={Ruizhi Deng and Bo Chang and Marcus A. Brubaker and Greg Mori and Andreas M. Lehrmann},
  booktitle=NeurIPS,
  year={2020}
}

@inproceedings{Continuous_Latent_Flows,
  title={{Continuous Latent Process Flows}},
  author={Ruizhi Deng and and Marcus A. Brubaker and Greg Mori and Andreas M. Lehrmann},
  booktitle=NeurIPS,
  year={2021}
}

@inproceedings{scalable_SDE,
  title={{Scalable Gradients for Stochastic Differential Equations}},
  author={Xuechen Li and Ting-Kam Leonard Wong and Ricky T. Q. Chen and David Duvenaud},
  booktitle=AISTATS,
  year={2020}
}
@inproceedings{latent_ode,
  title={{Latent ODEs for Irregularly-Sampled Time Series}},
  author={Yulia Rubanova and Ricky T. Q. Chen and David Duvenaud},
  booktitle= NeurIPS,
  year={2019}
}

@inproceedings{SVGD,
  title={Stein {V}ariational {G}radient {D}escent: {A} {G}eneral {P}urpose {B}ayesian {I}nference {A}lgorithm},
  author={Qiang Liu and Dilin Wang},
  booktitle=NeurIPS,
  year={2016}
}

@article{Nutz_22_a,
  author  = {Marcel Nutz and Johannes Wiesel},
  title   = {{Stability of Schrödinger Potentials and Convergence of Sinkhorn's Algorithm}},
  journal = {Annals of Probability},
  year    = {2022}
}

@article{exp_convergence_general_cost,
  author  = {Giacomo Greco and Maxence Noble and Giovanni Conforti and Alain Durmus},
  title   = {{Non-asymptotic Convergence Bounds for Sinkhorn Iterates and Their Gradients: a Coupling Approach}},
  journal = {arXiv:2304.06549},
  year    = {2023}
}



@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},
  booktitle=AISTAT,
  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},
  author={Holden Lee and Andrej Risteski and Rong Ge},
  booktitle=NeurIPS,
  year={2018}
}

@inproceedings{lin17,
  title={{R}untime {N}eural {P}runing},
  author={Ji Lin and Yongming Rao and Jiwen Lu and Jie Zhou},
  booktitle=NeurIPS,
  year={2017}
}


@inproceedings{Liwan13,
  author = {Li Wan and Matthew Zeiler and Sixin Zhang and Yann LeCun and Rob Fergus},
  booktitle = ICML,
  title = {Regularization of neural networks using dropconnect},
  year = {2013}
}

@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},
} 



@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},
}


@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,
  title = 	 {Variable {S}election via {P}enalized {N}eural {N}etwork: a {D}rop-{O}ut-{O}ne {L}oss {A}pproach},
  author = 	 {Ye, Mao and Sun, Yan},
  booktitle = 	 ICML,
  pages = 	 {5620--5629},
  year = 	 {2018},
  volume = 	 {80},
  month = 	 {10--15 Jul},
}

@inproceedings{Ahn12,
  author = {Sungjin Ahn and Anoop Korattikara and Max Welling},
  booktitle = ICML,
  title = {{B}ayesian {P}osterior {S}ampling via {S}tochastic {G}radient {F}isher {S}coring},
  year = {2012}
}


@article{Amodei16,
   author = {Dario Amodei and Chris Olah and Jacob Steinhardt and Paul Christiano and John Schulman and Dan Man{\'e}},
    title = {Concrete {P}roblems in {AI} {S}afety},
  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
for training tikhonov regularized deep neural networks},
  booktitle = NeurIPS,
  month = dec,
  year      = {2017}
}

@inproceedings{Yarin16b,
  author    = {Yarin Gal and Zoubin Ghahramani},
  title     = {A theoretically grounded application of dropout in recurrent neural networks},
  booktitle = NeurIPS,
  pages = {1019–1027},
  month = dec,
  year      = {2016}
}

@article{Dempster77,
 author = {Arthur Dempster and Nan Laird and Donald Rubin},
 journal = {Journal of the Royal Statistical Society. Series B},
 number = {1},
 pages = {1--38},
 publisher = {[Royal Statistical Society, Wiley]},
 title = {Maximum {L}ikelihood from {I}ncomplete {D}ata via the {EM} {A}lgorithm},
 volume = {39},
 year = {1977}
}

@article{andrieu05,
 author = {Christophe Andrieu and \'{E}ric Moulines and Pierre Priouret},
 journal = {SIAM J. Control Optim.},
 number = {1},
 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{score_sde,
  author    = {Yang Song and Jascha Sohl-Dickstein and Diederik P. Kingma and Abhishek Kumar and Stefano Ermon and Ben Poole},
  title     = {{Score-Based Generative Modeling through Stochastic Differential Equations
}},
  booktitle = ICLR,
  year      = {2021}
}

@inproceedings{song_likelihood_training,
  author    = {Yang Song and C. Durkan and I. Murray and Stefano Ermon},
  title     = {{Maximum Likelihood Training of Score-Based Diffusion Models
}},
  booktitle = NeurIPS,
  year      = {2021}
}

@inproceedings{DSB,
  author    = {De Bortoli, Valentin and  Thornton, James and  Heng, Jeremy and Doucet, Arnaud},
  title     = {{Diffusion Schr\"{o}dinger Bridge with Applications to Score-Based Generative Modeling}},
  booktitle = NeurIPS,
  year      = {2021}
}

@article{Chen21,
 author = {Chen, Yongxin and Georgiou, Tryphon T. and Pavon, Michele},
 journal = {SIAM Review},
 number = {2},
 pages = {249-313},
 title = {{Stochastic Control Liaisons: Richard Sinkhorn Meets Gaspard Monge on a Schr\"{o}dinger Bridge}},
 volume = {63},
 year = {2021}
}


@article{Hutchinson89,
 author = {Michael F. Hutchinson},
 journal = {Communications in Statistics-Simulation and Computation},
 number = {3},
 pages = {1059–1076},
 title = {{A Stochastic Estimator of the Trace of the Influence Matrix for Laplacian
Smoothing Splines}},
 volume = {18},
 year = {1989}
}


@inproceedings{gefei_21,
  author    = {Gefei Wang and Yuling Jiao and Qian Xu and Yang Wang and Can Yang},
  title     = {{Deep Generative Learning via Schr\"{o}dinger Bridge}},
  booktitle = ICML,
  year      = {2021}
}



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

@inproceedings{Riemannian_score_matching,
  author    = {James Thornton and Michael Hutchinson and Emile Mathieu and  De Bortoli, Valentin and Yee Whye Teh and Arnaud Doucet},
  title     = {{Riemannian Diffusion Schr\"{o}dinger Bridge}},
  booktitle = ICML,
  year      = {2022}
}

@article{Kullback_68,
  title={{Probability Densities with Given Marginals}},
  author={S. Kullback},
  journal={Ann. Math. Statist.},
  year={1968}
}

@article{IPF_95,
  title={{Convergence of the Iterative Proportional
Fitting Procedure}},
  author={L. Ruschendorf},
  journal={Ann. of Statistics},
  year={1995}
}





@inproceedings{DDPM,
  author    = {Jonathan Ho and Ajay Jain and Pieter Abbeel},
  title     = {{Denoising Diffusion Probabilistic Models}},
  booktitle = NeurIPS,
  year      = {2020}
}

@inproceedings{nonequilibrium_thermodynamics_15,
  author    = {Jascha Sohl-Dickstein and Eric A. Weiss and Niru Maheswaranathan and Surya Ganguli},
  title     = {{Deep Unsupervised Learning using Nonequilibrium Thermodynamics}},
  booktitle = ICML,
  year      = {2015}
}















% 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},
 journal = {SIAM J. Multiscale Modeling \& Simulation},
 title = {On the {I}nfinite {S}wapping {L}imit for {P}arallel {T}empering},
 volume = {10},
 Issue = {3},
 year = {2012}
}

@article{Neal01,
 author = {Radford M Neal.},
 journal = {Statistics and computing},
 title = {Annealed {I}mportance {S}ampling},
 volume = {11},
 Issue = {2},
 pages = {125-139},
 year = {2001}
}


@article{Rectified,
 author = {Qiang Liu},
 journal = {arXiv:2209.14577},
 title = {{Rectified Flow: A Marginal Preserving Approach to Optimal Transport}},
 year = {2022}
}

@article{osher_MFG_GAN,
 author = {Alex Tong Lin and Samy Wu Fung and Wuchen Li and Levon Nurbekyan and Stanley J. Osher},
 journal = {Proceedings of the National Academy of Sciences (PNAS)},
 title = {{Alternating the Population and Control Neural Networks to Solve High-Dimensional Stochastic Mean-Field Games}},
 volume = {118(31)},
 year = {2021}
}

@inproceedings{Rectified_group,
 author = {Xingchao Liu and Chengyue Gong and Qiang Liu},
 booktitle = ICLR,
 title = {{Flow Straight and Fast: Learning to Generate and Transfer Data with Rectified Flow}},
 year = 2023
}

@inproceedings{Albergo_stochastic_interpolants,
 author = {Michael S. Albergo and Eric Vanden-Eijnden},
 booktitle = ICLR,
 title = {{Building Normalizing Flows with Stochastic Interpolants}},
 year = 2023
}

@article{prob_flow_FPE,
 author = {Nicholas M. Boffi and Eric Vanden-Eijnden},
 journal = {arXiv:2206.04642},
 title = {{Probability Flow Solution of The Fokker-Planck Equation}},
 pages = {1-35},
 year = {2023}
}

@article{Albergo_unified_framework,
 author = {Michael S. Albergo and Nicholas M. Bof and Eric Vanden-Eijnden},
 journal = {arXiv:2303.08797v1},
 title = {{Stochastic Interpolants: A Unifying Framework for Flows and Diffusions}},
 pages = {1-48},
 year = {2023}
}


@article{awsgld,
 author = {Wei Deng and Guang Lin and Faming Liang},
 journal = {Statistics and Computing},
 title = {{An Adaptively Weighted Stochastic Gradient MCMC Algorithm for Monte Carlo Simulation and Global Optimization}},
 pages = {32-58},
 year = {2022}
}


@article{Neal01,
 author = {Radford M Neal.},
 journal = {Statistics and computing},
 title = {Annealed {I}mportance {S}ampling},
 volume = {11},
 Issue = {2},
 pages = {125-139},
 year = {2001}
}

@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{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,
 author = {T. Weinhart and A. Singh and A.R. Thornton},
 journal = {Slides},
 title = {Perturbation {T}heory \& {S}tability {A}nalysis},
  year = {2010}
}


@article{PhysRevLett86,
  title = {Replica {M}onte {C}arlo {S}imulation of {S}pin-{G}lasses},
  author = {Swendsen, Robert H. and Wang, Jian-Sheng},
  journal = {Physical Review Letters},
  volume = {57},
  issue = {21},
  pages = {2607--2609},
  numpages = {0},
  year = {1986},
}

@article{PhysRevLett85,
  title = {Bosonic {L}attice {G}auge {T}heory with {N}oise},
  author = {Gyan V. Bhanot and Anthony D. Kennedy},
  journal = {Physics Letters B},
  volume = {157B},
  issue = {1},
  pages = {70-76},
  year = {1985},
}

@article{VollmerZW2016,
  author  = {Sebastian J. Vollmer and Konstantinos C. Zygalakis and Yee Whye Teh},
  title   = {Exploration of the ({N}on-) {A}symptotic {B}ias and {V}ariance of {S}tochastic {G}radient {L}angevin {D}ynamics},
  journal = {Journal of Machine Learning Research},
  year    = {2016},
  volume  = {17},
  number  = {159},
  pages   = {1-48},
}




@article{Reflected_brownian_motion,
  title={{Reflected Brownian Motion with Skew Symmetric
Data in a Polyhedral Domain}},
  author={Williams, R. J.},
  issues = {75(4)},
  pages = {1432-2064},
  journal={Probability Theory
and Related Fields},
  year={1987}
}

@article{proj_LMC,
  title={{Sampling from a Log-Concave Distribution with Projected Langevin Monte Carlo}},
  author={S\'{e}bastien Bubeck and Ronen Eldan and Joseph Lehec},
  volume  = {59(1)},
  journal={Discrete \& Computational Geometry},
  year={2018}
}

@article{sinkhorn_exp_general,
  title={{Quantitative Contraction Rates for Sinkhorn Algorithm: Beyond Bounded Costs and Compact Marginals}},
  author={Giovanni Conforti and Alain Durmus and Giacomo Greco},
  journal={arXiv:2304.04451},
  year={2023}
}



@inproceedings{Proximal_LMC,
  title={{Sampling from a Log-concave Distribution with Compact Support with Proximal Langevin Monte Carlo}},
  author={Nicolas Brosse and Alain Durmus and \'{E}ric Moulines and Marcelo Pereyra},
  booktitle={COLT},
  year={2017}
}

@inproceedings{mirror_LMC,
  title={{Mirrored Langevin Dynamics}},
  author={Ya-Ping Hsieh and  Ali Kavis and Paul Rolland and Volkan Cevher},
  booktitle=NeurIPS,
  year={2018}
}




@article{wong97,
  title = {Dynamic {W}eighting in {M}onte {C}arlo and {O}ptimization},
  author = {Wing Hung Wong and Faming Liang},
  journal = {Proc. Natl. Acad. Sci.},
  volume = {94},
  issue = {26},
  pages = {14220-14224},
  year = {1997},
}

@article{Geyer91,
  Author = {Geyer, Charles J.},
  Title = {Markov {C}hain {M}onte {C}arlo {M}aximum {L}ikelihood},
  Journal = { Computing Science and
Statistics: Proceedings of the 23rd Symposium on the Interfac},
  Year = {1991},
  Pages = {156--163},
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  pages = {581-587},
}

@article{leli2008,
  author = {T. Leli\`{e}vre and M. Rousset and G. Stoltz},
  title = {Long-time {C}onvergence of an {A}daptive {B}iasing {F}orce {M}ethod},
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  volume = {21},
  pages = {1155–1181},
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@article{Fort15,
 author = {G. Fort and B. Jourdain and E. Kuhn and T. Lelièvre and G. Stoltz},
 journal = {Math. Comput.},
 pages = {2297–2327},
 title = {Convergence of the {W}ang-{L}andau {A}lgorithm},
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@article{RobbinsM1951,
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}

@article{RobertsRosenthal2007,
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  pages = {458-475}
}

@article{Gelman97,
 author={A. Gelman and W. R. Gilks and G. O. Roberts},
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 year={1997},
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}

@article{Alain17,
 author={Alain Durmus and \'{E}ric Moulines},
 journal={Annals of Applied Probability},
 title={Non-asymptotic {C}onvergence {A}nalysis for the {U}nadjusted {L}angevin {A}lgorithm
},
 year={2017},
 volume={27},
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@inproceedings{Mackey18,
  title={Global {N}on-convex {O}ptimization with {D}iscretized {D}iffusions},
  author={Murat A Erdogdu and Lester Mackey and Ohad Shamir},
  booktitle=NeurIPS,
  year={2018}
}


@article{AndrieuMoulines2006,
 author={Christophe Andrieu and \'{E}ric Moulines},
 journal={Annals of Applied Probability},
 title={On the {E}rgodicity {P}roperties of {S}ome {A}daptive {MCMC} {A}lgorithms},
 year={2006},
 volume={16},
 pages={1462-1505}
}

@article{Pelletier98,
 author={Mariane Pelletier},
 journal={Annals of Applied Probability},
 title={Weak {C}onvergence {R}ates for {S}tochastic {A}pproximation with {A}pplication to {M}ultiple {T}argets and {S}imulated {A}nnealing},
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@article{Fortetal2011,
 author={Fort, G. and \'{E}. Moulines and P. Priouret},
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 year={2011},
 volume={39},
 pages={3262-3289}
}

@article{Pseudo-Marginal-method,
 author={Christophe Andrieu and Gareth O. Roberts},
 journal={Annals of Statistics},
 title={The {P}seudo-{M}arginal {A}pproach for {E}fficient {M}onte {C}arlo {C}omputations},
 year={2009},
 volume={37},
 pages={697-725}
}

@inproceedings{Sato2014ApproximationAO,
  title={Approximation {A}nalysis of {S}tochastic {G}radient {L}angevin {D}ynamics by {U}sing {F}okker-{P}lanck {E}quation and {I}to {P}rocess},
  author={Issei Sato and Hiroshi Nakagawa},
  booktitle=ICML,
  year={2014}
}







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@book{Pavliotis14,
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@book{Neal96,
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@book{oksendal2003stochastic,
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@book{liujun,
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@book{Pinsker,
  title={Information {T}heory: {C}oding {T}heorems for {D}iscrete {M}emoryless {S}ystems},
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  year={2011},
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@book{yin_zhu_10,
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@book{Robert04,
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@book{Albert90,
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@book{log_concave_sampling,
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@book{Goodfellow16,
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@book{Gelman13,
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year={2013},
month=nov,
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@book{Compute_OT,
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publisher = {Foundations and Trends\@ in
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title={{Optimal Transport for Applied Mathematicians: 
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year={2015},
publisher = {Springer}
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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,
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title={{S}tatistical learning with sparsity:  The lasso and
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publisher = {CRC press}
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@book{Resnick02,
author = {Resnick, Sidney I.},
title={Adventures in {S}tochastic {P}rocesses},
year={2002},
publisher = {Springer}
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@book{Le16,
author = {Jean-Fran\cedilla{c}ois Le Gall},
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publisher = {Springer}
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@book{Liptser01,
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title={{Statistics of Random Processes: I. General Theory}},
year={2001},
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@book{Karatzas_Shreve,
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  publisher={American Mathematical Soc.}
}


@book{Villani03,
  title={{Topics in Optimal Transportation}},
  author={C\'{e}dric Villani},
  volume={58},
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  publisher={American Mathematical Soc.}
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@book{Ma_FB_SDE,
  title={{Forward-Backward Stochastic Differential Equations and their Applications}},
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@book{Evans_PDE,
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@inproceedings{forward_backward_SDE,
 author = {Tianrong Chen and Guan-Horng Liu and Evangelos A. Theodorou},
 title = {{Likelihood Training of Schr\"{o}dinger Bridge using Forward-Backward SDEs Theory}},
 booktitle = ICLR,
 year = {2022}
}

@article{Anderson82,
author={Brian D.O. Anderson},
title={{Reverse-time Diffusion Equation Models}},
journal={Stochastic Processes and Their Applications},
year={1982},
volume={12},
number={3},
pages={313-326}
}