@inproceedings{langley00,
 author    = {P. Langley},
 title     = {Crafting Papers on Machine Learning},
 year      = {2000},
 pages     = {1207--1216},
 editor    = {Pat Langley},
 booktitle     = {Proceedings of the 17th International Conference
              on Machine Learning (ICML 2000)},
 address   = {Stanford, CA},
 publisher = {Morgan Kaufmann}
}

@TechReport{mitchell80,
  author = 	 "T. M. Mitchell",
  title = 	 "The Need for Biases in Learning Generalizations",
  institution =  "Computer Science Department, Rutgers University",
  year = 	 "1980",
  address =	 "New Brunswick, MA",
}

@phdthesis{kearns89,
  author = {M. J. Kearns},
  title =  {Computational Complexity of Machine Learning},
  school = {Department of Computer Science, Harvard University},
  year =   {1989}
}

@Book{MachineLearningI,
  editor = 	 "R. S. Michalski and J. G. Carbonell and T.
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  year = 	 "1983",
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}

@Book{DudaHart2nd,
  author =       "R. O. Duda and P. E. Hart and D. G. Stork",
  title =        "Pattern Classification",
  publisher =    "John Wiley and Sons",
  edition =      "2nd",
  year =         "2000"
}

@misc{anonymous,
  title= {Suppressed for Anonymity},
  author= {Author, N. N.},
  year= {2021}
}

@InCollection{Newell81,
  author =       "A. Newell and P. S. Rosenbloom",
  title =        "Mechanisms of Skill Acquisition and the Law of
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  pages =        "1--51",
  publisher =    "Lawrence Erlbaum Associates, Inc.",
  year =         "1981",
  editor =       "J. R. Anderson",
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}


@Article{Samuel59,
  author = 	 "A. L. Samuel",
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		  Checkers",
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  year =	 "1959",
  volume =	 "3",
  number =	 "3",
  pages =	 "211--229"
}

@incollection{Bengio+chapter2007,
author = {Bengio, Yoshua and LeCun, Yann},
booktitle = {Large Scale Kernel Machines},
publisher = {MIT Press},
title = {Scaling Learning Algorithms Towards {AI}},
year = {2007}
}

@article{Hinton06,
author = {Hinton, Geoffrey E. and Osindero, Simon and Teh, Yee Whye},
journal = {Neural Computation},
pages = {1527--1554},
title = {A Fast Learning Algorithm for Deep Belief Nets},
volume = {18},
year = {2006}
}

@book{goodfellow2016deep,
title={Deep learning},
author={Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron and Bengio, Yoshua},
volume={1},
year={2016},
publisher={MIT Press}
}

@article{bubeck2018sampling,
  title={Sampling from a log-concave distribution with projected langevin monte carlo},
  author={Bubeck, S{\'e}bastien and Eldan, Ronen and Lehec, Joseph},
  journal={Discrete \& Computational Geometry},
  volume={59},
  pages={757--783},
  year={2018},
  publisher={Springer}
}


%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/

%% Created for Michael N. Arbel at 2021-03-08 20:00:44 +0000 

@inproceedings{Agakov2004,
  title={An auxiliary variational method},
  author={Agakov, Felix V and Barber, David},
  booktitle={Advances in Neural Information Processing Systems},
  year={2004},
}

@inproceedings{Masrani2019,
 author = {Masrani, Vaden and Le, Tuan Anh and Wood, Frank},
 booktitle = {Advances in Neural Information Processing Systems},
 pages = {},
 title = {The Thermodynamic Variational Objective},
 year = {2019}
}

@inproceedings{Burda2015,
  title={Importance Weighted Autoencoders},
  author={Burda, Yuri and Grosse, Roger B and Salakhutdinov, Ruslan},
  booktitle={International Conference on Learning Representations},
  year={2016}
}

@InProceedings{Bilos2021,
  title = 	 {Scalable Normalizing Flows for Permutation Invariant Densities},
  author =       {Bilo{\v{s}}, Marin and G{\"u}nnemann, Stephan},
  booktitle = 	 {Proceedings of the 38th International Conference on Machine Learning},
  pages = 	 {957--967},
  year = 	 {2021},
  editor = 	 {Meila, Marina and Zhang, Tong},
  volume = 	 {139},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {18--24 Jul},
  publisher =    {PMLR}
}


@InProceedings{Lee2019,
  title = 	 {Set Transformer: A Framework for Attention-based Permutation-Invariant Neural Networks},
  author =       {Lee, Juho and Lee, Yoonho and Kim, Jungtaek and Kosiorek, Adam and Choi, Seungjin and Teh, Yee Whye},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {3744--3753},
  year = 	 {2019},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--15 Jun},
  publisher =    {PMLR}
}


@inproceedings{Dockhorn2022,
title={Score-Based Generative Modeling with Critically-Damped {L}angevin Diffusion},
author={Tim Dockhorn and Arash Vahdat and Karsten Kreis},
booktitle={International Conference on Learning Representations},
year={2022}
}

@InProceedings{Greff2019,
  title = 	 {Multi-Object Representation Learning with Iterative Variational Inference},
  author =       {Greff, Klaus and Kaufman, Rapha{\"e}l Lopez and Kabra, Rishabh and Watters, Nick and Burgess, Christopher and Zoran, Daniel and Matthey, Loic and Botvinick, Matthew and Lerchner, Alexander},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {2424--2433},
  year = 	 {2019},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--15 Jun},
  publisher =    {PMLR}
}

@inproceedings{Matthews2022,
  author = {Matthews, Alexander G. D. G. and Arbel, Michael and Rezende, Danilo J. and Doucet, Arnaud},
  title = {Continual Repeated Annealed Flow Transport {M}onte {C}arlo},
  booktitle={International Conference on Machine Learning},
  year = {2022},
}

@InProceedings{Arbel2021,
  title = 	 {Annealed Flow Transport {M}onte {C}arlo},
  author =       {Arbel, Michael and Matthews, Alex G.D.G. and Doucet, Arnaud},
  booktitle = 	 {International Conference on Machine Learning},
  year = 	 {2021},
}

@article{Opper2019,
author = {Opper, Manfred},
year = {2019},
month = {01},
pages = {1800233},
title = {Variational Inference for Stochastic Differential Equations},
volume = {531},
journal = {Annalen der Physik},
doi = {10.1002/andp.201800233}
}

@InProceedings{Cornish2020,
  title = 	 {Relaxing Bijectivity Constraints with Continuously Indexed Normalising Flows},
  author =       {Cornish, Rob and Caterini, Anthony and Deligiannidis, George and Doucet, Arnaud},
  booktitle = 	 {International Conference on Machine Learning},
  year = 	 {2020},
}

@article{ba2016layer,
  title={Layer normalization},
  author={Ba, Jimmy Lei and Kiros, Jamie Ryan and Hinton, Geoffrey E},
  journal={arXiv preprint arXiv:1607.06450},
  year={2016}
}



@article{ramachandran2017searching,
  title={Searching for activation functions},
  author={Ramachandran, Prajit and Zoph, Barret and Le, Quoc V},
  journal={arXiv preprint arXiv:1710.05941},
  year={2017}
}

@article{dinh2014nice,
  title={Nice: Non-linear independent components estimation},
  author={Dinh, Laurent and Krueger, David and Bengio, Yoshua},
  journal={arXiv preprint arXiv:1410.8516},
  year={2014}
}


@InProceedings{Middleton2019,
  title = 	 {Unbiased smoothing using particle independent {M}etropolis--{H}astings},
  author =       {Middleton, Lawrence and Deligiannidis, George and Doucet, Arnaud and Jacob, Pierre E.},
  booktitle = 	 {Artificial Intelligence and Statistics},
  year = 	 {2019},
}


@article{Andrieu2011,
author = {Andrieu, Christophe and Doucet, Arnaud and Holenstein, Roman},
title = {Particle {M}arkov chain {M}onte {C}arlo methods},
journal = {Journal of the Royal Statistical Society: Series \textup{B}},
volume = {72},
number = {3},
pages = {269-342},
year = {2010}
}

@article{Syed2019,
  title={Non-reversible parallel tempering: a scalable highly parallel {MCMC} scheme},
  author={Syed, Saifuddin and Bouchard-C{\^o}t{\'e}, Alexandre and Deligiannidis, George and Doucet, Arnaud},
  journal={arXiv preprint arXiv:1905.02939},
  year={2019}
}

@article{DeHaan2021,
  title={Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows},
  author={de Haan, Pim and Rainone, Corrado and Cheng, Miranda and Bondesan, Roberto},
  journal={arXiv preprint arXiv:2110.02673},
  year={2021}
}



@inproceedings{Dinh2017,
  author    = {Laurent Dinh and
               Jascha Sohl{-}Dickstein and
               Samy Bengio},
  title     = {Density estimation using Real {NVP}},
  booktitle = {International Conference on Learning Representations},
  year      = {2017}
}

@article{Albergo2021,
  title={Introduction to Normalizing Flows for Lattice Field Theory},
  author={Albergo, Michael S and Boyda, Denis and Hackett, Daniel C and Kanwar, Gurtej and Cranmer, Kyle and Racani{\`e}re, S{\'e}bastien and Rezende, Danilo Jimenez and Shanahan, Phiala E},
  journal={arXiv preprint arXiv:2101.08176},
  year={2021}
}

@article{Albergo2019,
  title = {Flow-based generative models for {M}arkov chain {M}onte {C}arlo in lattice field theory},
  author = {Albergo, Michael S. and Kanwar, Gurtej and Shanahan, Phiala E.},
  journal = {Physical Review \textup{D}},
  volume = {100},
  issue = {3},
  pages = {034515},
  numpages = {13},
  year = {2019},
}

@ARTICLE{Borsanyi2021,
       author = {{Borsanyi}, Sz. and {Fodor}, Z. and {Guenther}, J.~N. and {Hoelbling}, C. and {Katz}, S.~D. and {Lellouch}, L. and {Lippert}, T. and {Miura}, K. and {Parato}, L. and {Szabo}, K.~K. and {Stokes}, F. and {Toth}, B.~C. and {Torok}, Cs. and {Varnhorst}, L.},
        title = "{Leading hadronic contribution to the muon magnetic moment from lattice QCD}",
      journal = {Nature},
      year = 2021,
       volume = {593},
       number = {7857},
        pages = {51-55},
}


@article{Duane1987,
title = {Hybrid {M}onte {C}arlo},
author={Duane, Simon and Kennedy, Anthony D and Pendleton, Brian J and Roweth, Duncan},
journal = {Physics Letters \textup{B}},
volume = {195},
number = {2},
pages = {216-222},
year = {1987},
}

@misc{Hoffman2019,
      title={NeuTra-lizing Bad Geometry in Hamiltonian Monte Carlo Using Neural Transport}, 
      author={Matthew Hoffman and Pavel Sountsov and Joshua V. Dillon and Ian Langmore and Dustin Tran and Srinivas Vasudevan},
      year={2019},
      eprint={1903.03704},
      archivePrefix={arXiv},
      primaryClass={stat.CO}
}


@inproceedings{Grosse2013,
 author = {Grosse, Roger B and Maddison, Chris J and Salakhutdinov, Russ R},
 booktitle = {Advances in Neural Information Processing Systems},
 title = {Annealing between distributions by averaging moments},
 year = {2013}
}






@InCollection{turner+sahani:2011a,
  author = 	 {R. E. Turner and M. Sahani},
  title = 	 {Two problems with variational expectation
                  maximisation for time-series models},
  booktitle = 	 {Bayesian Time Series Models},
  pages = 	 {109--130},
  publisher = {Cambridge University Press},
  year = 	 2011,
  editor = 	 {D. Barber and T. Cemgil and S. Chiappa},
  chapter = 	 5
}

@InProceedings{Hoffman:2017, title = {Learning Deep Latent {G}aussian Models with {M}arkov Chain {M}onte {C}arlo}, author = {Matthew D. Hoffman}, booktitle = {Proceedings of the 34th International Conference on Machine Learning}, pages = {1510--1519}, year = {2017}, editor = {Precup, Doina and Teh, Yee Whye}, volume = {70}, series = {Proceedings of Machine Learning Research}, month = {06--11 Aug}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v70/hoffman17a/hoffman17a.pdf}}

%% Saved with string encoding Unicode (UTF-8) 
@ARTICLE{Ba2016,
       author = {{Lei Ba}, Jimmy and {Kiros}, Jamie Ryan and {Hinton}, Geoffrey E.},
        title = "{Layer Normalization}",
      journal = {arXiv e-prints},
     keywords = {Statistics - Machine Learning, Computer Science - Machine Learning},
         year = 2016,
        month = jul,
       eprint = {1607.06450}
}




@inproceedings{Wu:2017,
  author    = {Yuhuai Wu and
               Yuri Burda and
               Ruslan Salakhutdinov and
               Roger B. Grosse},
  title     = {On the Quantitative Analysis of Decoder-Based Generative Models},
  booktitle = {International Conference on Learning Representations},
  year      = {2017},
}

@inproceedings{Salakhutdinov:2008,
  title={On the quantitative analysis of {D}eep {B}elief {N}etworks},
  author={Ruslan Salakhutdinov and Iain Murray},
  booktitle={Proceedings of the 25th Annual International Conference on Machine Learning (ICML 2008)},
  pages={872--879},
  year={2008}
}

@article{Sen:2018a,
	Author = {Sen, Bodhisattva},
	Title = {A Gentle Introduction to Empirical Process Theory and Applications},
	Journal={Lecture Notes, Columbia University},
	Year={2018}}

@book{Dudley:2018,
	Author = {Dudley, Richard M},
	Date-Added = {2021-03-08 14:31:26 +0000},
	Date-Modified = {2021-03-08 14:31:26 +0000},
	Publisher = {CRC Press},
	Title = {Real analysis and Probability},
	Year = {2018},}


@article{gao2020flow,
	Author = {Gao, Christina and Isaacson, Joshua and Krause, Claudius},
	Journal = {arXiv preprint arXiv:2001.05486},
	Title = {i-flow: High-dimensional {I}ntegration and {S}ampling with Normalizing Flows},
	Year = {2020}}

@inproceedings{Germain:15,
	Author = {Mathieu Germain and Karol Gregor and Iain Murray and Hugo Larochelle},
	Booktitle = {International Conference on Machine Learning},
	Year = {2015}}

@article{Choi:2019,
	Author = {Choi, Michael CH},
	Journal = {arXiv preprint arXiv:1907.10318},
	Title = {Universality of the {L}angevin diffusion as scaling limit of a family of {M}etropolis--{H}astings processes I: fixed dimension},
	Year = {2019}}

@article{Gelfand:1991,
	Author = {Gelfand, Saul Brian and Mitter, Sanjoy K},
	Date-Added = {2020-10-27 17:06:24 +0000},
	Date-Modified = {2020-10-27 17:06:24 +0000},
	Journal = {Journal of Optimization Theory and Applications},
	Number = {3},
	Pages = {483--498},
	Publisher = {Springer},
	Title = {Weak convergence of {M}arkov chain sampling methods and annealing algorithms to diffusions},
	Volume = {68},
	Year = {1991}}

@article{Del-Moral:2012,
	Author = {Del Moral, Pierre and Doucet, Arnaud and Jasra, Ajay},
	Journal = {Bernoulli},
	Number = {1},
	Pages = {252--278},
	Publisher = {Bernoulli Society for Mathematical Statistics and Probability},
	Title = {On adaptive resampling strategies for sequential {M}onte {C}arlo methods},
	Volume = {18},
	Year = {2012}}

@book{Van-der-Vaart:2000,
	Author = {Van der Vaart, Aad W},
	Publisher = {Cambridge University Press},
	Title = {Asymptotic Statistics},
	Year = {2000}}

@article{Douc:2007,
	Author = {Douc, Randal and Moulines, Eric},
	Journal = {The Annals of Statistics},
	Number = {5},
	Pages = {2344--2376},
	Publisher = {Institute of Mathematical Statistics},
	Title = {Limit theorems for weighted samples with applications to sequential {M}onte {C}arlo methods},
	Volume = {36},
	Year = {2008}}

@article{Chauveau:2013,
	Author = {Chauveau, Didier and Vandekerkhove, Pierre},
	Date-Added = {2020-08-27 10:12:55 +0000},
	Date-Modified = {2020-08-27 10:12:55 +0000},
	Journal = {ESAIM: Probability and Statistics},
	Pages = {419--431},
	Title = {Smoothness of {M}etropolis--{H}astings algorithm and application to entropy estimation},
	Volume = {17},
	Year = {2013}}

@book{Pollard:1984,
	Author = {Pollard, David},
	Date-Added = {2020-08-26 15:29:12 +0000},
	Date-Modified = {2020-08-26 15:29:12 +0000},
	Publisher = {Springer Science \& Business Media},
	Title = {Convergence of stochastic processes},
	Year = {1984}}


@inproceedings{Pollard:1990,
	Author = {Pollard, David},
	Booktitle = {NSF-CBMS regional conference series in probability and statistics},
	Date-Added = {2020-08-26 15:29:01 +0000},
	Date-Modified = {2020-08-26 15:29:01 +0000},
	Organization = {JSTOR},
	Pages = {i--86},
	Title = {Empirical processes: theory and applications},
	Year = {1990}}

@article{Beskos:2016,
	Author = {Beskos, Alexandros and Jasra, Ajay and Kantas, Nikolas and Thiery, Alexandre},
	Journal = {The Annals of Applied Probability},
	Number = {2},
	Pages = {1111--1146},
	Publisher = {Institute of Mathematical Statistics},
	Title = {On the convergence of adaptive sequential {M}onte {C}arlo methods},
	Volume = {26},
	Year = {2016}}

@article{Dalalyan:2014,
	Author = {Dalalyan, Arnak S},
	Journal = {Journal of the Royal Statistical Society: Series \textup{B}},
	Number = {79},
	Pages = {651--676},
	Title = {Theoretical guarantees for approximate sampling from smooth and log-concave densities},
	Volume = {3},
	Year = {2017}}

@book{Del-Moral:2013a,
	Author = {Del Moral, Pierre},
	Date-Added = {2020-07-14 10:42:15 +0000},
	Date-Modified = {2020-07-14 10:42:15 +0000},
	Publisher = {CRC press},
	Title = {Mean Field Simulation for Monte Carlo Integration},
	Year = {2013}}

@article{Del-Moral:2013,
	Author = {Del Moral, Pierre and Jacob, Pierre E and Lee, Anthony and Murray, Lawrence and Peters, Gareth W},
	Journal = {Stochastic Analysis and Applications},
	Number = {5},
	Pages = {830--871},
	Title = {Feynman-Kac particle integration with geometric interacting jumps},
	Volume = {31},
	Year = {2013}}

@article{Moral:2007,
	Author = {Moral, P Del and Miclo, L},
	Date-Added = {2020-07-14 10:42:15 +0000},
	Date-Modified = {2020-07-14 10:42:15 +0000},
	Journal = {Stochastic analysis and applications},
	Number = {3},
	Pages = {519--575},
	Publisher = {Taylor \& Francis},
	Title = {Strong Propagations of Chaos in Moran's Type Particle Interpretations of Feynman--Kac Measures},
	Volume = {25},
	Year = {2007}}

@book{Del-Moral:2000b,
	Author = {Del Moral, Pierre and Miclo, Laurent},
	Date-Added = {2020-07-14 10:42:15 +0000},
	Date-Modified = {2020-07-14 10:42:15 +0000},
	Publisher = {Universit{\'e} de Toulouse. Laboratoire de Statistique et Probabilit{\'e}s [LSP]},
	Title = {About the strong propagation of chaos for interacting particle approximations of Feynman-Kac formulae},
	Year = {2000}}

@article{Del-Moral:2000a,
	Author = {Del Moral, Pierre and Miclo, Laurent},
	Date-Added = {2020-07-14 10:42:15 +0000},
	Date-Modified = {2020-07-14 10:42:15 +0000},
	Journal = {Stochastic processes and their applications},
	Number = {2},
	Pages = {193--216},
	Publisher = {Elsevier},
	Title = {A Moran particle system approximation of Feynman--Kac formulae},
	Volume = {86},
	Year = {2000}}

@incollection{Del-Moral:2000,
	Author = {Del Moral, Pierre and Miclo, Laurent},
	Booktitle = {Seminaire de probabilites XXXIV},
	Date-Added = {2020-07-14 10:42:15 +0000},
	Date-Modified = {2020-07-14 10:42:15 +0000},
	Pages = {1--145},
	Publisher = {Springer},
	Title = {Branching and interacting particle systems approximations of Feynman-Kac formulae with applications to non-linear filtering},
	Year = {2000}}

@inproceedings{Hairer:2011,
	Author = {Hairer, Martin and Mattingly, Jonathan C},
	Booktitle = {Seminar on Stochastic Analysis, Random Fields and Applications VI},
	Date-Added = {2020-07-14 10:41:25 +0000},
	Date-Modified = {2020-07-14 10:41:25 +0000},
	Organization = {Springer},
	Pages = {109--117},
	Title = {Yet another look at {H}arris' ergodic theorem for {M}arkov chains},
	Year = {2011}}

@article{Ferre:2019,
	Author = {Ferr{\'e}, Gr{\'e}goire and Stoltz, Gabriel},
	Date-Added = {2020-07-14 10:39:55 +0000},
	Date-Modified = {2020-07-14 10:39:55 +0000},
	Journal = {Numerische Mathematik},
	Number = {2},
	Pages = {261--313},
	Publisher = {Springer},
	Title = {Error estimates on ergodic properties of discretized {F}eynman--{K}ac semigroups},
	Volume = {143},
	Year = {2019}}

@article{Ferre:2018,
	Author = {Ferr{\'e}, Gr{\'e}goire and Rousset, Mathias and Stoltz, Gabriel},
	Date-Added = {2020-07-14 08:38:19 +0000},
	Date-Modified = {2020-07-14 08:38:19 +0000},
	Journal = {arXiv preprint arXiv:1807.00390},
	Title = {More on the long time stability of {F}eynman-{K}ac semigroups},
	Year = {2018}}

@article{Gerber:2015,
	Author = {Gerber, Mathieu and Whiteley, Nick},
	Date-Added = {2020-07-14 08:35:28 +0000},
	Date-Modified = {2020-07-14 08:35:31 +0000},
	Journal = {arXiv preprint arXiv:1512.04834},
	Title = {Stability with respect to initial conditions in V-norm for nonlinear filters with ergodic observations},
	Year = {2015}}

@book{Ambrosio:2008,
	Abstract = {Gradient Flows...},
	Author = {Ambrosio, Luigi and Gigli, Nicola and Savare, Giuseppe},
	Date-Added = {2020-06-25 22:46:26 +0000},
	Date-Modified = {2020-06-25 22:46:26 +0000},
	Edition = {2},
	Isbn = {978-3-7643-8721-1},
	Language = {en},
	Publisher = {Birkh{\"a}user Basel},
	Series = {Lectures in {Mathematics}. {ETH} {Z{\"u}rich}},
	Shorttitle = {Gradient {Flows}},
	Title = {Gradient {Flows}: {In} {Metric} {Spaces} and in the {Space} of {Probability} {Measures}},
	Url = {https://www.springer.com/us/book/9783764387211},
	Urldate = {2019-05-14},
	Year = {2008},
	Bdsk-Url-1 = {https://www.springer.com/us/book/9783764387211}}

@book{Pham:2009,
	Author = {Pham, Huy{\^e}n},
	Date-Added = {2020-06-25 22:35:14 +0000},
	Date-Modified = {2020-06-25 22:35:14 +0000},
	Publisher = {Springer Science \& Business Media},
	Title = {Continuous-time stochastic control and optimization with financial applications},
	Volume = {61},
	Year = {2009}}

@article{Jarzynski:1997,
	Author = {Jarzynski, Christopher},
	Date-Added = {2020-06-25 14:06:00 +0000},
	Date-Modified = {2020-06-25 14:06:00 +0000},
	Journal = {Physical Review E},
	Number = {5},
	Pages = {5018},
	Publisher = {APS},
	Title = {Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach},
	Volume = {56},
	Year = {1997}}

@article{Steinwart:2007a,
	Abstract = {For binary classification we establish learning rates up to the order of \$n{\textasciicircum}\{-1\}\$ for support vector machines (SVMs) with hinge loss and Gaussian RBF kernels. These rates are in terms of two assumptions on the considered distributions: Tsybakov's noise assumption to establish a small estimation error, and a new geometric noise condition which is used to bound the approximation error. Unlike previously proposed concepts for bounding the approximation error, the geometric noise assumption does not employ any smoothness assumption.},
	Annote = {Comment: Published at http://dx.doi.org/10.1214/009053606000001226 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)},
	Author = {Steinwart, Ingo and Scovel, Clint},
	Date-Added = {2020-03-24 15:04:41 +0000},
	Date-Modified = {2020-03-24 15:04:41 +0000},
	Doi = {10.1214/009053606000001226},
	File = {arXiv Fulltext PDF:/Users/MichaelArbel/Zotero/storage/TWHYPXCL/Steinwart and Scovel - 2007 - Fast rates for support vector machines using Gauss.pdf:application/pdf;arXiv.org Snapshot:/Users/MichaelArbel/Zotero/storage/857JSMG9/0708.html:text/html},
	Issn = {0090-5364},
	Journal = {The Annals of Statistics},
	Keywords = {62G20, 62G99, 68T05, 68T10, 41A46, 41A99 (Secondary), 68Q32 (Primary), Mathematics - Statistics Theory, Statistics - Machine Learning},
	Month = apr,
	Note = {arXiv: 0708.1838},
	Number = {2},
	Pages = {575--607},
	Title = {Fast rates for support vector machines using {Gaussian} kernels},
	Url = {http://arxiv.org/abs/0708.1838},
	Urldate = {2020-03-01},
	Volume = {35},
	Year = {2007},
	Bdsk-Url-1 = {http://arxiv.org/abs/0708.1838},
	Bdsk-Url-2 = {https://doi.org/10.1214/009053606000001226}}

@book{Doucet:2001,
	Address = {New York},
	Author = {Doucet, Arnaud and Freitas, Nando de and Gordon, Neil},
	Date-Added = {2020-03-24 15:02:45 +0000},
	Date-Modified = {2020-03-24 15:02:45 +0000},
	Doi = {10.1007/978-1-4757-3437-9},
	File = {Snapshot:/Users/MichaelArbel/Zotero/storage/JC4NLITM/9780387951461.html:text/html},
	Isbn = {978-0-387-95146-1},
	Language = {en},
	Publisher = {Springer-Verlag},
	Series = {Information {Science} and {Statistics}},
	Title = {Sequential {Monte} {Carlo} {Methods} in {Practice}},
	Url = {https://www.springer.com/gp/book/9780387951461},
	Urldate = {2019-12-28},
	Year = {2001},
	Bdsk-Url-1 = {https://www.springer.com/gp/book/9780387951461},
	Bdsk-Url-2 = {https://doi.org/10.1007/978-1-4757-3437-9}}

@article{Lu:2019,
	Abstract = {A fundamental problem in Bayesian inference and statistical machine learning is to efficiently sample from multimodal distributions. Due to metastability, multimodal distributions are difficult to sample using standard Markov chain Monte Carlo methods. We propose a new sampling algorithm based on a birth-death mechanism to accelerate the mixing of Langevin diffusion. Our algorithm is motivated by its mean field partial differential equation (PDE), which is a Fokker-Planck equation supplemented by a nonlocal birth-death term. This PDE can be viewed as a gradient flow of the Kullback-Leibler divergence with respect to the Wasserstein-Fisher-Rao metric. We prove that under some assumptions the asymptotic convergence rate of the nonlocal PDE is independent of the potential barrier, in contrast to the exponential dependence in the case of the Langevin diffusion. We illustrate the efficiency of the birth-death accelerated Langevin method through several analytical examples and numerical experiments.},
	Author = {Lu, Yulong and Lu, Jianfeng and Nolen, James},
	Date-Added = {2020-03-18 11:01:17 +0000},
	Date-Modified = {2020-03-18 11:01:19 +0000},
	Journal = {arXiv:1905.09863 [cs, math, stat]},
	Keywords = {Computer Science - Machine Learning, Mathematics - Analysis of PDEs, Mathematics - Statistics Theory, Statistics - Machine Learning},
	Month = may,
	Note = {arXiv: 1905.09863},
	Title = {Accelerating {Langevin} {Sampling} with {Birth}-death},
	Url = {http://arxiv.org/abs/1905.09863},
	Urldate = {2020-03-18},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1905.09863}}

@article{Rousset:2006,
	Abstract = {We present some applications of an Interacting Particle System (IPS) methodology to the field of Molecular Dynamics. This IPS method allows several simulations of a switched random process to keep closer to equilibrium at each time, thanks to a selection mechanism based on the relative virtual work induced on the system. It is therefore an efficient improvement of usual non-equilibrium simulations, which can be used to compute canonical averages, free energy differences, and typical transitions paths.},
	Author = {Rousset, Mathias and Stoltz, Gabriel},
	Journal = {Journal of Statistical Physics},
	Month = jun,
	Number = {6},
	Pages = {1251--1272},
	Title = {Equilibrium sampling from nonequilibrium dynamics},
	Urldate = {2020-01-03},
	Volume = {123},
	Year = {2006}}

@article{Simsekli:2020,
	Abstract = {Stochastic gradient descent with momentum (SGDm) is one of the most popular optimization algorithms in deep learning. While there is a rich theory of SGDm for convex problems, the theory is considerably less developed in the context of deep learning where the problem is non-convex and the gradient noise might exhibit a heavy-tailed behavior, as empirically observed in recent studies. In this study, we consider a {\textbackslash}emph\{continuous-time\} variant of SGDm, known as the underdamped Langevin dynamics (ULD), and investigate its asymptotic properties under heavy-tailed perturbations. Supported by recent studies from statistical physics, we argue both theoretically and empirically that the heavy-tails of such perturbations can result in a bias even when the step-size is small, in the sense that {\textbackslash}emph\{the optima of stationary distribution\} of the dynamics might not match {\textbackslash}emph\{the optima of the cost function to be optimized\}. As a remedy, we develop a novel framework, which we coin as {\textbackslash}emph\{fractional\} ULD (FULD), and prove that FULD targets the so-called Gibbs distribution, whose optima exactly match the optima of the original cost. We observe that the Euler discretization of FULD has noteworthy algorithmic similarities with {\textbackslash}emph\{natural gradient\} methods and {\textbackslash}emph\{gradient clipping\}, bringing a new perspective on understanding their role in deep learning. We support our theory with experiments conducted on a synthetic model and neural networks.},
	Annote = {Comment: 26 pages},
	Author = {{\c S}im{\c s}ekli, Umut and Zhu, Lingjiong and Teh, Yee Whye and G{\"u}rb{\"u}zbalaban, Mert},
	Date-Added = {2020-03-10 13:28:45 +0000},
	Date-Modified = {2020-03-10 13:28:48 +0000},
	File = {arXiv Fulltext PDF:/Users/MichaelArbel/Zotero/storage/XNZ6I5LA/{\c S}im{\c s}ekli et al. - 2020 - Fractional Underdamped Langevin Dynamics Retarget.pdf:application/pdf;arXiv.org Snapshot:/Users/MichaelArbel/Zotero/storage/R7JJW88H/2002.html:text/html},
	Journal = {arXiv:2002.05685 [cs, stat]},
	Keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
	Month = feb,
	Note = {arXiv: 2002.05685},
	Shorttitle = {Fractional {Underdamped} {Langevin} {Dynamics}},
	Title = {Fractional {Underdamped} {Langevin} {Dynamics}: {Retargeting} {SGD} with {Momentum} under {Heavy}-{Tailed} {Gradient} {Noise}},
	Url = {http://arxiv.org/abs/2002.05685},
	Urldate = {2020-03-10},
	Year = {2020},
	Bdsk-Url-1 = {http://arxiv.org/abs/2002.05685}}

@article{Simon-Gabriel:2016,
	Author = {Carl-Johann Simon-Gabriel and Bernhard Sch{{\"o}}lkopf},
	Journal = {Journal of Machine Learning Research},
	Number = {44},
	Pages = {1-29},
	Title = {Kernel Distribution Embeddings: Universal Kernels, Characteristic Kernels and Kernel Metrics on Distributions},
	Url = {http://jmlr.org/papers/v19/16-291.html},
	Volume = {19},
	Year = {2018},
	Bdsk-Url-1 = {http://jmlr.org/papers/v19/16-291.html}}

@misc{cvx,
	Author = {Michael Grant and Stephen Boyd},
	Howpublished = {\url{http://cvxr.com/cvx}},
	Month = mar,
	Title = {{CVX}: Matlab Software for Disciplined Convex Programming, version 2.1},
	Year = {2014}}

@incollection{gb08,
	Author = {Michael Grant and Stephen Boyd},
	Booktitle = {Recent Advances in Learning and Control},
	Pages = {95--110},
	Publisher = {Springer-Verlag Limited},
	Series = {Lecture Notes in Control and Information Sciences},
	Title = {Graph implementations for nonsmooth convex programs},
	Year = {2008}}

@article{Retherford:1978,
	Author = {Retherford, J. R.},
	Date-Added = {2020-02-16 14:27:03 +0000},
	Date-Modified = {2020-02-16 14:27:03 +0000},
	Fjournal = {Bulletin of the American Mathematical Society},
	Journal = {Bull. Amer. Math. Soc.},
	Month = {07},
	Number = {4},
	Pages = {681--685},
	Publisher = {American Mathematical Society},
	Title = {Review: J. Diestel and J. J. Uhl, Jr., Vector measures},
	Url = {http://projecteuclid.org/euclid.bams/1183540941},
	Volume = {84},
	Year = {1978},
	Bdsk-Url-1 = {http://projecteuclid.org/euclid.bams/1183540941}}

@book{Ekeland:1999,
	Author = {Ekeland, I. and T{\'e}mam, R.},
	Month = {01},
	Publisher = {Society for Industrial and Applied Mathematics},
	Series = {Classics in {Applied} {Mathematics}},
	Title = {Convex {Analysis} and {Variational} {Problems}},
	Url = {https://epubs.siam.org/doi/book/10.1137/1.9781611971088},
	Urldate = {2019-08-24},
	Year = {1999},
	Bdsk-Url-1 = {https://epubs.siam.org/doi/book/10.1137/1.9781611971088}}

@inproceedings{Wenliang:2018,
	Abstract = {The kernel exponential family is a rich class of distributions, which can be fit efficiently and with statistical guarantees by score matching. Being required to choose a priori a simple kernel suc...},
	Author = {Wenliang, Li and Sutherland, Dougal and Strathmann, Heiko and Gretton, Arthur},
	Booktitle = {International {Conference} on {Machine} {Learning}},
	Month = may,
	Pages = {6737--6746},
	Title = {Learning deep kernels for exponential family densities},
	Url = {http://proceedings.mlr.press/v97/wenliang19a.html},
	Urldate = {2020-02-07},
	Year = {2019},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v97/wenliang19a.html}}

@inproceedings{Arbel:2018a,
	Abstract = {A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families  using functional parameters in a suitable RKHS. An algorithm is provided for l...},
	Author = {Arbel, Michael and Gretton, Arthur},
	Booktitle = {International {Conference} on {Artificial} {Intelligence} and {Statistics}},
	Language = {en},
	Month = mar,
	Pages = {1337--1346},
	Title = {Kernel {Conditional} {Exponential} {Family}},
	Url = {http://proceedings.mlr.press/v84/arbel18a.html},
	Urldate = {2020-02-07},
	Year = {2018},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v84/arbel18a.html}}

@inproceedings{Sutherland:2018,
	Abstract = {We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite dimen...},
	Author = {Sutherland, Dougal and Strathmann, Heiko and Arbel, Michael and Gretton, Arthur},
	Booktitle = {International {Conference} on {Artificial} {Intelligence} and {Statistics}},
	Date-Added = {2020-02-07 11:40:34 +0000},
	Date-Modified = {2020-02-07 11:40:37 +0000},
	File = {Full Text PDF:/Users/MichaelArbel/Zotero/storage/CQF9H7WK/Sutherland et al. - 2018 - Efficient and principled score estimation with Nys.pdf:application/pdf;Snapshot:/Users/MichaelArbel/Zotero/storage/ZA6VDJM6/sutherland18a.html:text/html},
	Language = {en},
	Month = mar,
	Pages = {652--660},
	Title = {Efficient and principled score estimation with {Nystr{\"o}m} kernel exponential families},
	Url = {http://proceedings.mlr.press/v84/sutherland18a.html},
	Urldate = {2020-02-07},
	Year = {2018},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v84/sutherland18a.html}}

@inproceedings{Rezende:2015,
	Author = {Rezende, Danilo Jimenez and Mohamed, Shakir},
	Booktitle = {International Conference on Machine Learning},
	Title = {Variational inference with normalizing flows},
	Year = {2015}}

@article{kingma+welling:2014,
	Author = {Kingma, Diederik P. and Welling, Max},
	Journal = {International Conference on Learning Representations},
	Title = {Auto-Encoding Variational {B}ayes},
	Year = 2014}

@inproceedings{rezende+al:2014:icml,
	Author = {Rezende, Danilo Jimenez and Mohamed, Shakir and Wierstra, Daan},
	Booktitle = {International Conference on Machine Learning},
	Title = {Stochastic Backpropagation and Approximate Inference in Deep Generative Models},
	Year = 2014}

@inbook{LecChoHadMArFu06,
	Author = {Yann LeCun and Sumit Chopra and Raia Hadsell and Marc'Aurelio Ranzato and Fu-Jie Huang},
	Chapter = {A Tutorial on Energy-Based Learning},
	Publisher = {MIT Press},
	Title = {Predicting Structured Data},
	Year = {2006}}

@article{Sturm:1998,
	Author = {Sturm, K. T.},
	Issn = {0091-1798, 2168-894X},
	Journal = {The Annals of Probability},
	Language = {en},
	Month = jan,
	Mrnumber = {MR1617040},
	Number = {1},
	Pages = {1--55},
	Title = {Diffusion processes and heat kernels on metric spaces},
	Url = {https://projecteuclid.org/euclid.aop/1022855410},
	Urldate = {2020-02-07},
	Volume = {26},
	Year = {1998},
	Bdsk-Url-1 = {https://projecteuclid.org/euclid.aop/1022855410}}

@article{Sriperumbudur:2009a,
	Author = {Bharath K. Sriperumbudur and Kenji Fukumizu and Arthur Gretton and Bernhard Sch{\"o}lkopf and Gert R. G. Lanckriet},
	Eprint = {0901.2698},
	Month = {01},
	Title = {On integral probability metrics, {\"I}-divergences and binary classification},
	Url = {https://arxiv.org/abs/0901.2698},
	Year = {2009},
	Bdsk-Url-1 = {https://arxiv.org/abs/0901.2698}}

@misc{Fukumizu:2009,
	Author = {Fukumizu, K.},
	Journal = {Algebraic and Geometric Methods in Statistics},
	Language = {en},
	Month = oct,
	Title = {Exponential manifold by reproducing kernel {Hilbert} spaces},
	Year = {2009}}

@article{Canu:2006,
	Author = {Canu, St{\'e}phane and Smola, Alex},
	Journal = {Neurocomput.},
	Keywords = {Exponential families, Kernel methods, Novelty detection},
	Month = mar,
	Number = {7-9},
	Numpages = {7},
	Pages = {714--720},
	Publisher = {Elsevier Science Publishers B. V.},
	Title = {Kernel Methods and the Exponential Family},
	Url = {http://dx.doi.org/10.1016/j.neucom.2005.12.009},
	Volume = {69},
	Year = {2006},
	Bdsk-Url-1 = {http://dx.doi.org/10.1016/j.neucom.2005.12.009}}

@incollection{Jordan:1999,
	Address = {Cambridge, MA, USA},
	Author = {Jordan, Michael I. and Ghahramani, Zoubin and Jaakkola, Tommi S. and Saul, Lawrence K.},
	Booktitle = {Learning in graphical models},
	Date-Added = {2020-02-06 15:06:11 +0000},
	Date-Modified = {2020-02-06 15:06:12 +0000},
	Isbn = {978-0-262-60032-3},
	Month = feb,
	Pages = {105--161},
	Publisher = {MIT Press},
	Title = {An introduction to variational methods for graphical models},
	Urldate = {2020-02-06},
	Year = {1999}}

@article{Wainwright:2008,
	Abstract = {Graphical Models, Exponential Families, and Variational Inference},
	Author = {Wainwright, Martin J. and Jordan, Michael I.},
	Journal = {Foundations and Trends{\textregistered} in Machine Learning},
	Language = {English},
	Month = nov,
	Number = {1--2},
	Pages = {1--305},
	Title = {Graphical {Models}, {Exponential} {Families}, and {Variational} {Inference}},
	Volume = {1},
	Year = {2008},}

@article{Candes:2005,
	Author = {Cand{\`e}s, Emmanuel and Romberg, Justin and Tao, Terence},
	Journal = {Communications on Pure and Applied Mathematics},
	Month = {08},
	Title = {Stable Signal Recovery from Incomplete and Inaccurate Measurements},
	Volume = {59},
	Year = {2006}}

@article{Donoho:2006,
	Author = {D. L. {Donoho}},
	Issn = {1557-9654},
	Journal = {IEEE Transactions on Information Theory},
	Month = {April},
	Number = {4},
	Pages = {1289-1306},
	Title = {Compressed sensing},
	Volume = {52},
	Year = {2006}}

@article{Bolic:2005,
	Journal = {IEEE Transactions on Signal Processing},
	Keywords = {Algorithms for parallel implementation, distributed algorithms, distributed particle filter, distributed resampling, distributed resampling algorithm, field programmable gate array, field programmable gate arrays, Field programmable gate arrays, Filtering, FPGA implementation, Frequency, importance sampling, interconnection network, Multiprocessor interconnection networks, nonproportional allocation, parallel architecture, parallel architectures, Parallel architectures, parallel implementation, Parallel processing, particle filter, Particle filters, processing element, proportional allocation, RNA, sampling importance resampling, Sampling methods, Scalability, signal sampling},
	Month = jul,
	Number = {7},
	Pages = {2442--2450},
	Title = {Resampling algorithms and architectures for distributed particle filters},
	Volume = {53},
	Year = {2005}}

@inproceedings{Arora:2017,
	Author = {Sanjeev Arora and Rong Ge and Yingyu Liang and Tengyu Ma and Yi Zhang},
	Booktitle = {Proceedings of the 34th International Conference on Machine Learning},
	Month = {06--11 Aug},
	Pages = {224--232},
	Pdf = {http://proceedings.mlr.press/v70/arora17a/arora17a.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {Generalization and Equilibrium in Generative Adversarial Nets ({GAN}s)},
	Url = {http://proceedings.mlr.press/v70/arora17a.html},
	Volume = {70},
	Year = {2017},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v70/arora17a.html}}

@article{Wu:2019b,
	Author = {Wu, Yan and Donahue, Jeff and Balduzzi, David and Simonyan, Karen and Lillicrap, Timothy},
	Journal = {arXiv:1912.00953 [cs, stat]},
	Keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
	Month = dec,
	Note = {arXiv: 1912.00953},
	Shorttitle = {{LOGAN}},
	Title = {{LOGAN}: {Latent} {Optimisation} for {Generative} {Adversarial} {Networks}},
	Url = {http://arxiv.org/abs/1912.00953},
	Urldate = {2020-01-18},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1912.00953}}

@inproceedings{Wu:2019c,
	Address = {Long Beach, California, USA},
	Author = {Wu, Yan and Rosca, Mihaela and Lillicrap, Timothy},
	Booktitle = {Proceedings of the 36th International Conference on Machine Learning},
	Month = {09--15 Jun},
	Pages = {6850--6860},
	Pdf = {http://proceedings.mlr.press/v97/wu19d/wu19d.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {Deep Compressed Sensing},
	Url = {http://proceedings.mlr.press/v97/wu19d.html},
	Volume = {97},
	Year = {2019},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v97/wu19d.html}}

@incollection{Lawson:2020,
	Author = {Lawson, John and Tucker, George and Dai, Bo and Ranganath, Rajesh},
	Booktitle = {Advances in Neural Information Processing Systems 32},
	Pages = {8501--8513},
	Publisher = {Curran Associates, Inc.},
	Title = {Energy-Inspired Models: Learning with Sampler-Induced Distributions},
	Url = {https://arxiv.org/abs/1910.14265},
	Year = {2019},
	Bdsk-Url-1 = {https://arxiv.org/abs/1910.14265}}

@inproceedings{Azadi:2019,
	Author = {Samaneh Azadi and Catherine Olsson and Trevor Darrell and Ian Goodfellow and Augustus Odena},
	Booktitle = {International Conference on Learning Representations},
	Title = {Discriminator Rejection Sampling},
	Url = {https://openreview.net/forum?id=S1GkToR5tm},
	Year = {2019},
	Bdsk-Url-1 = {https://openreview.net/forum?id=S1GkToR5tm}}

@article{Ding:2019,
	Author = {Ding, Xin and Wang, Z. Jane and Welch, William J.},
	Shorttitle = {Subsampling {Generative} {Adversarial} {Networks}},
	Title = {Subsampling {Generative} {Adversarial} {Networks}: {Density} {Ratio} {Estimation} in {Feature} {Space} with {Softplus} {Loss}},
	Url = {http://arxiv.org/abs/1909.10670},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1909.10670}}

@article{Song:2019,
	Author = {Song, Jiaming and Ermon, Stefano},
	Journal = {arXiv:1910.09779 [cs, stat]},
	Month = oct,
	Note = {arXiv: 1910.09779},
	Title = {Bridging the {Gap} {Between} \$f\$-{GANs} and {Wasserstein} {GANs}},
	Url = {http://arxiv.org/abs/1910.09779},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1910.09779}}

@incollection{Heusel:2017,
	Author = {Heusel, Martin and Ramsauer, Hubert and Unterthiner, Thomas and Nessler, Bernhard and Hochreiter, Sepp},
	Booktitle = {Advances in Neural Information Processing Systems 30},
	Pages = {6626--6637},
	Publisher = {Curran Associates, Inc.},
	Title = {GANs Trained by a Two Time-Scale Update Rule Converge to a Local Nash Equilibrium},
	Url = {https://arxiv.org/abs/1706.08500},
	Year = {2017},
	Bdsk-Url-1 = {https://arxiv.org/abs/1706.08500}}

@inproceedings{Radford:2015,
	Author = {Alec Radford and Luke Metz and Soumith Chintala},
	Bibsource = {dblp computer science bibliography, https://dblp.org},
	Biburl = {https://dblp.org/rec/journals/corr/RadfordMC15.bib},
	Booktitle = {4th International Conference on Learning Representations, {ICLR} 2016, San Juan, Puerto Rico, May 2-4, 2016, Conference Track Proceedings},
	Timestamp = {Thu, 25 Jul 2019 14:25:38 +0200},
	Title = {Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks},
	Url = {http://arxiv.org/abs/1511.06434},
	Year = {2016},
	Bdsk-Url-1 = {http://arxiv.org/abs/1511.06434}}

@techreport{Krizhevsky:2009,
	Author = {Alex Krizhevsky},
	Institution = {University of Toronto},
	Title = {Learning multiple layers of features from tiny images},
	Year = {2009}}

@article{Germain:2015,
	Author = {Germain, Mathieu and Gregor, Karol and Murray, Iain and Larochelle, Hugo},
	Date = {2015-06-05},
	Eprint = {1502.03509},
	Eprinttype = {arxiv},
	Journal = {ICML},
	Shorttitle = {{MADE}},
	Title = {{MADE}: Masked Autoencoder for Distribution Estimation},
	Url = {http://arxiv.org/abs/1502.03509},
	Urldate = {2020-02-05},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1502.03509}}

@article{Papamakarios:2017,
	Author = {Papamakarios, George and Pavlakou, Theo and Murray, Iain},
	Eprint = {1705.07057},
	Eprinttype = {arxiv},
	File = {arXiv Fulltext PDF:/Users/MichaelArbel/Zotero/storage/TA3MQ4FU/Papamakarios et al. - 2018 - Masked Autoregressive Flow for Density Estimation.pdf:application/pdf;arXiv.org Snapshot:/Users/MichaelArbel/Zotero/storage/92ECNUYT/1705.html:text/html},
	Journal = {NIPS},
	Keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
	Title = {Masked Autoregressive Flow for Density Estimation},
	Url = {http://arxiv.org/abs/1705.07057},
	Urldate = {2020-02-05},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1705.07057}}

@article{Dinh:2016,
	Abstract = {Unsupervised learning of probabilistic models is a central yet challenging problem in machine learning. Specifically, designing models with tractable learning, sampling, inference and evaluation is crucial in solving this task. We extend the space of such models using real-valued non-volume preserving (real NVP) transformations, a set of powerful invertible and learnable transformations, resulting in an unsupervised learning algorithm with exact log-likelihood computation, exact sampling, exact inference of latent variables, and an interpretable latent space. We demonstrate its ability to model natural images on four datasets through sampling, log-likelihood evaluation and latent variable manipulations.},
	Author = {Laurent Dinh and Jascha Sohl-Dickstein and Samy Bengio},
	Eprint = {1605.08803},
	Month = {05},
	Title = {Density estimation using Real NVP},
	Url = {https://arxiv.org/abs/1605.08803},
	Year = {2016},
	Bdsk-Url-1 = {https://arxiv.org/abs/1605.08803}}


@inproceedings{Turner:2019a,
	Address = {Long Beach, California, USA},
	Author = {Turner, Ryan and Hung, Jane and Frank, Eric and Saatchi, Yunus and Yosinski, Jason},
	Booktitle = {Proceedings of the 36th International Conference on Machine Learning},
	Month = {09--15 Jun},
	Pages = {6345--6353},
	Pdf = {http://proceedings.mlr.press/v97/turner19a/turner19a.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {{M}etropolis-{H}astings Generative Adversarial Networks},
	Url = {http://proceedings.mlr.press/v97/turner19a.html},
	Volume = {97},
	Year = {2019},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v97/turner19a.html}}

@incollection{Grover:2019,
	Author = {Grover, Aditya and Song, Jiaming and Kapoor, Ashish and Tran, Kenneth and Agarwal, Alekh and Horvitz, Eric J and Ermon, Stefano},
	Booktitle = {Advances in Neural Information Processing Systems 32},
	Pages = {11058--11070},
	Publisher = {Curran Associates, Inc.},
	Title = {Bias Correction of Learned Generative Models using Likelihood-Free Importance Weighting},
	Url = {https://arxiv.org/abs/1906.09531},
	Year = {2019},
	Bdsk-Url-1 = {https://arxiv.org/abs/1906.09531}}

@incollection{Tanaka:2019,
	Author = {Tanaka, Akinori},
	Booktitle = {Advances in {Neural} {Information} {Processing} {Systems} 32},
	File = {NIPS Full Text PDF:/Users/MichaelArbel/Zotero/storage/L7973RI5/Tanaka - 2019 - Discriminator optimal transport.pdf:application/pdf;NIPS Snapshot:/Users/MichaelArbel/Zotero/storage/TM2APQKM/8906-discriminator-optimal-transport.html:text/html},
	Pages = {6813--6823},
	Publisher = {Curran Associates, Inc.},
	Title = {Discriminator optimal transport},
	Url = {http://papers.nips.cc/paper/8906-discriminator-optimal-transport.pdf},
	Urldate = {2020-02-04},
	Year = {2019},
	Bdsk-Url-1 = {http://papers.nips.cc/paper/8906-discriminator-optimal-transport.pdf}}

@inproceedings{Dai:2018,
	Author = {Dai, Bo and Dai, Hanjun and Gretton, Arthur and Song, Le and Schuurmans, Dale and He, Niao},
	Booktitle = {Proceedings of Machine Learning Research},
	Month = {16--18 Apr},
	Pages = {2321--2330},
	Pdf = {http://proceedings.mlr.press/v89/dai19a/dai19a.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {Kernel Exponential Family Estimation via Doubly Dual Embedding},
	Url = {http://proceedings.mlr.press/v89/dai19a.html},
	Volume = {89},
	Year = {2019},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v89/dai19a.html}}

@article{Dai:2019,
	Author = {Dai, Bo and Liu, Zhen and Dai, Hanjun and He, Niao and Gretton, Arthur and Song, Le and Schuurmans, Dale},
	Journal = {arXiv:1904.12083 [cs, stat]},
	Keywords = {Computer Science - Machine Learning, Statistics - Computation, Statistics - Machine Learning},
	Month = dec,
	Note = {arXiv: 1904.12083},
	Title = {Exponential {Family} {Estimation} via {Adversarial} {Dynamics} {Embedding}},
	Url = {http://arxiv.org/abs/1904.12083},
	Urldate = {2020-01-26},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1904.12083}}

@incollection{Sanjabi:2018,
	Author = {Sanjabi, Maziar and Ba, Jimmy and Razaviyayn, Meisam and Lee, Jason D},
	Booktitle = {Advances in Neural Information Processing Systems 31},
	Pages = {7091--7101},
	Publisher = {Curran Associates, Inc.},
	Title = {On the Convergence and Robustness of Training GANs with Regularized Optimal Transport},
	Url = {https://arxiv.org/abs/1802.08249},
	Year = {2018},
	Bdsk-Url-1 = {https://arxiv.org/abs/1802.08249}}

@inproceedings{Arjovsky:2017a,
	Abstract = {We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to different distances between distributions.},
	Address = {International Convention Centre, Sydney, Australia},
	Author = {Martin Arjovsky and Soumith Chintala and L{\'e}on Bottou},
	Booktitle = {Proceedings of the 34th International Conference on Machine Learning},
	Month = {06--11 Aug},
	Pages = {214--223},
	Pdf = {http://proceedings.mlr.press/v70/arjovsky17a/arjovsky17a.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {{W}asserstein Generative Adversarial Networks},
	Url = {http://proceedings.mlr.press/v70/arjovsky17a.html},
	Volume = {70},
	Year = {2017},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v70/arjovsky17a.html}}

@inproceedings{Arjovsky:2017,
	Author = {Martin Arjovsky and L{\'e}on Bottou},
	Booktitle = {International Conference on Learning Representations},
	Title = {Towards Principled Methods for Training Generative Adversarial Networks},
	Year = {2017}}

@article{Milgrom:2002,
	Author = {Milgrom, Paul and Segal, Ilya},
	File = {Full Text PDF:/Users/MichaelArbel/Zotero/storage/HAZV4VRQ/Milgrom and Segal - 2002 - Envelope Theorems for Arbitrary Choice Sets.pdf:application/pdf;Snapshot:/Users/MichaelArbel/Zotero/storage/IPA7QY5A/1468-0262.html:text/html},
	Issn = {1468-0262},
	Journal = {Econometrica},
	Keywords = {differentiable value function, envelope theorem, math programming, mechanism design, sensitivity analysis},
	Language = {en},
	Number = {2},
	Pages = {583--601},
	Title = {Envelope {Theorems} for {Arbitrary} {Choice} {Sets}},
	Url = {https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00296},
	Urldate = {2020-01-30},
	Volume = {70},
	Year = {2002},
	Bdsk-Url-1 = {https://onlinelibrary.wiley.com/doi/abs/10.1111/1468-0262.00296}}

@article{Sachs:2017,
	Author = {Sachs, Matthias and Leimkuhler, Benedict and Danos, Vincent},
	Journal = {Entropy},
	Keywords = {fluctuation-dissipation theorems, Langevin dynamics, local thermal equilibrium, molecular dynamics, nonequilibrium simulation, sampling, temperature gradients},
	Language = {en},
	Month = dec,
	Number = {12},
	Pages = {647},
	Shorttitle = {Langevin {Dynamics} with {Variable} {Coefficients} and {Nonconservative} {Forces}},
	Title = {Langevin {Dynamics} with {Variable} {Coefficients} and {Nonconservative} {Forces}: {From} {Stationary} {States} to {Numerical} {Methods}},
	Url = {https://www.mdpi.com/1099-4300/19/12/647},
	Urldate = {2020-01-29},
	Volume = {19},
	Year = {2017},
	Bdsk-Url-1 = {https://www.mdpi.com/1099-4300/19/12/647}}

@article{Eberle:2018,
	Author = {Eberle, Andreas and Guillin, Arnaud and Zimmer, Raphael},
	Journal = {The Annals of Probability},
	Title = {Couplings and quantitative contraction rates for {Langevin} dynamics},
	Url = {http://arxiv.org/abs/1703.01617},
	Urldate = {2020-01-29},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1703.01617}}

@article{Ma:2019,
	Author = {Ma, Yi-An and Chen, Yuansi and Jin, Chi and Flammarion, Nicolas and Jordan, Michael I.},
	Eprint = {https://www.pnas.org/content/116/42/20881.full.pdf},
	Issn = {0027-8424},
	Journal = {Proceedings of the National Academy of Sciences},
	Number = {42},
	Pages = {20881--20885},
	Publisher = {National Academy of Sciences},
	Title = {Sampling can be faster than optimization},
	Url = {https://www.pnas.org/content/116/42/20881},
	Volume = {116},
	Year = {2019},
	Bdsk-Url-1 = {https://www.pnas.org/content/116/42/20881}}

@article{Bubeck:2015,
	Author = {Bubeck, S{\'e}bastien and Eldan, Ronen and Lehec, Joseph},
	Date-Added = {2020-01-29 16:20:03 +0000},
	Date-Modified = {2020-01-29 16:20:10 +0000},
	File = {arXiv Fulltext PDF:/Users/MichaelArbel/Zotero/storage/M6Z4V3FF/Bubeck et al. - 2015 - Sampling from a log-concave distribution with Proj.pdf:application/pdf;arXiv.org Snapshot:/Users/MichaelArbel/Zotero/storage/QYZFK5CP/1507.html:text/html},
	Journal = {arXiv:1507.02564 [cs, math]},
	Keywords = {Computer Science - Data Structures and Algorithms, Computer Science - Machine Learning, Mathematics - Probability},
	Month = jul,
	Note = {arXiv: 1507.02564},
	Title = {Sampling from a log-concave distribution with {Projected} {Langevin} {Monte} {Carlo}},
	Url = {http://arxiv.org/abs/1507.02564},
	Urldate = {2020-01-29},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1507.02564}}

@incollection{Thekumparampil:2019,
	Author = {Thekumparampil, Kiran K and Jain, Prateek and Netrapalli, Praneeth and Oh, Sewoong},
	Booktitle = {Advances in Neural Information Processing Systems 32},
	Pages = {12680--12691},
	Publisher = {Curran Associates, Inc.},
	Title = {Efficient Algorithms for Smooth Minimax Optimization},
	Url = {http://arxiv.org/abs/1907.01543},
	Year = {2019},
	Bdsk-Url-1 = {http://arxiv.org/abs/1907.01543}}

@article{Davis:2018,
	Author = {Davis, Damek and Drusvyatskiy, Dmitriy},
	Journal = {arXiv:1802.02988 [cs, math]},
	Month = feb,
	Title = {Stochastic subgradient method converges at the rate \${O}(k{\textasciicircum}\{-1/4\})\$ on weakly convex functions},
	Url = {http://arxiv.org/abs/1802.02988},
	Year = {2018},
	Bdsk-Url-1 = {http://arxiv.org/abs/1802.02988}}

@incollection{Goodfellow:2014,
	Author = {Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua},
	Booktitle = {Advances in Neural Information Processing Systems 27},
	Pages = {2672--2680},
	Publisher = {Curran Associates, Inc.},
	Title = {Generative Adversarial Nets},
	Url = {http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf},
	Year = {2014},
	Bdsk-Url-1 = {http://papers.nips.cc/paper/5423-generative-adversarial-nets.pdf}}

@inproceedings{Chu:2019,
	Author = {Casey Chu and Kentaro Minami and Kenji Fukumizu},
	Booktitle = {International Conference on Learning Representations},
	Title = {Smoothness and Stability in GANs},
	Url = {https://openreview.net/forum?id=HJeOekHKwr},
	Year = {2020},
	Bdsk-Url-1 = {https://openreview.net/forum?id=HJeOekHKwr}}

@incollection{Nowozin:2016,
	Author = {Nowozin, Sebastian and Cseke, Botond and Tomioka, Ryota},
	Booktitle = {Advances in Neural Information Processing Systems 29},
	Pages = {271--279},
	Publisher = {Curran Associates, Inc.},
	Title = {f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization},
	Url = {https://arxiv.org/abs/1606.00709},
	Year = {2016},
	Bdsk-Url-1 = {https://arxiv.org/abs/1606.00709}}

@inproceedings{Arbel:2017,
	Abstract = {A nonparametric family of conditional distributions is introduced, which generalizes conditional exponential families  using functional parameters in a suitable RKHS. An algorithm is provided for learning the generalized natural parameter, and  consistency of the estimator is established in the well specified case. In experiments, the new method generally outperforms a competing approach with consistency guarantees, and is competitive with a deep conditional density model on datasets that exhibit abrupt transitions and heteroscedasticity.  },
	Address = {Playa Blanca, Lanzarote, Canary Islands},
	Author = {Michael Arbel and Arthur Gretton},
	Booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
	Month = {09--11 Apr},
	Pages = {1337--1346},
	Pdf = {http://proceedings.mlr.press/v84/arbel18a/arbel18a.pdf},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {Kernel Conditional Exponential Family},
	Url = {http://proceedings.mlr.press/v84/arbel18a.html},
	Volume = {84},
	Year = {2018},
	Bdsk-Url-1 = {http://proceedings.mlr.press/v84/arbel18a.html}}

@inproceedings{Sutherland:2017,
	Abstract = {We propose a fast method with statistical guarantees for learning an exponential family density model where the natural parameter is in a reproducing kernel Hilbert space, and may be infinite dimensional. The model is learned by fitting the derivative of the log density, the score, thus avoiding the need to compute a normalization constant. We improved the computational efficiency of an earlier solution with a low-rank, Nystr{\"o}m-like solution. The new solution retains the consistency and convergence rates of the full-rank solution (exactly in Fisher distance, and nearly in other distances), with guarantees on the degree of cost and storage reduction. We evaluate the method in experiments on density estimation and in the construction of an adaptive Hamiltonian Monte Carlo sampler. Compared to an existing score learning approach using a denoising autoencoder, our estimator is empirically more data-efficient when estimating the score, runs faster, and has fewer parameters (which can be tuned in a principled and interpretable way), in addition to providing statistical guarantees.},
	Address = {Playa Blanca, Lanzarote, Canary Islands},
	Author = {Dougal Sutherland and Heiko Strathmann and Michael Arbel and Arthur Gretton},
	Booktitle = {Proceedings of the Twenty-First International Conference on Artificial Intelligence and Statistics},
	Month = {09--11 Apr},
	Pages = {652--660},
	Publisher = {PMLR},
	Series = {Proceedings of Machine Learning Research},
	Title = {Efficient and principled score estimation with Nystr{\"o}m kernel exponential families},
	Url = {https://arxiv.org/abs/1705.08360},
	Volume = {84},
	Year = {2018},
	Bdsk-Url-1 = {https://arxiv.org/abs/1705.08360}}

@article{Sriperumbudur:2013,
	Author = {Bharath Sriperumbudur and Kenji Fukumizu and Revant Kumar and Arthur Gretton and Aapo Hyv{\"a}rinen},
	Eprint = {1312.3516},
	Journal = {Journal of Machine Learning Research},
	Month = {12},
	Title = {Density Estimation in Infinite Dimensional Exponential Families},
	Url = {https://arxiv.org/abs/1312.3516},
	Year = {2017},
	Bdsk-Url-1 = {https://arxiv.org/abs/1312.3516}}

@incollection{Du:2019,
	Author = {Du, Yilun and Mordatch, Igor},
	Booktitle = {Advances in Neural Information Processing Systems 32},
	Pages = {3608--3618},
	Publisher = {Curran Associates, Inc.},
	Title = {Implicit Generation and Modeling with Energy Based Models},
	Url = {https://arxiv.org/abs/1903.08689},
	Year = {2019},
	Bdsk-Url-1 = {https://arxiv.org/abs/1903.08689}}

@article{Hyvarinen:2005a,
	Author = {Hyv{\"a}rinen, Aapo},
	Journal = {The Journal of Machine Learning Research},
	Pages = {695--709},
	Title = {Estimation of non-normalized statistical models by score matching},
	Volume = {6},
	Year = {2005},
	}
	
@article{Gutmann:2012,
	Author = {Gutmann, Michael U. and Hyv{\"a}rinen, Aapo},
	Journal = {The Journal of Machine Learning Research},
	Keywords = {computation, estimation, natural image statistics, partition function, unnormalized models},
	Month = feb,
	Number = {null},
	Pages = {307--361},
	Title = {Noise-contrastive estimation of unnormalized statistical models, with applications to natural image statistics},
	Volume = {13},
	Year = {2012}}

@incollection{Uppal:2019,
	Author = {Uppal, Ananya and Singh, Shashank and Poczos, Barnabas},
	Booktitle = {Advances in Neural Information Processing Systems 32},
	Pages = {9089--9100},
	Publisher = {Curran Associates, Inc.},
	Title = {Nonparametric Density Estimation \&amp; Convergence Rates for GANs under Besov IPM Losses},
	Url = {http://papers.nips.cc/paper/9109-nonparametric-density-estimation-convergence-rates-for-gans-under-besov-ipm-losses.pdf},
	Year = {2019},
	Bdsk-Url-1 = {http://papers.nips.cc/paper/9109-nonparametric-density-estimation-convergence-rates-for-gans-under-besov-ipm-losses.pdf}}

@article{nguyen2010estimating,
	Author = {Nguyen, XuanLong and Wainwright, Martin J and Jordan, Michael I},
	Journal = {IEEE Transactions on Information Theory},
	Number = {11},
	Pages = {5847--5861},
	Publisher = {IEEE},
	Title = {Estimating divergence functionals and the likelihood ratio by convex risk minimization},
	Volume = {56},
	Year = {2010}}

@article{birge2000adaptive,
	Author = {Birg{\'e}, Lucien and Massart, Pascal},
	Journal = {Constructive Approximation},
	Number = {1},
	Pages = {1--36},
	Publisher = {Springer},
	Title = {An adaptive compression algorithm in Besov spaces},
	Volume = {16},
	Year = {2000}}

@article{bunch2016approximations,
	Author = {Bunch, Pete and Godsill, Simon},
	Journal = {Journal of the American Statistical Association},
	Number = {514},
	Pages = {748--762},
	Publisher = {Taylor \& Francis},
	Title = {Approximations of the optimal importance density using Gaussian particle flow importance sampling},
	Volume = {111},
	Year = {2016}}

@article{Marzouk2012bayesian,
	Author = {El Moselhy, Tarek A and Marzouk, Youssef M},
	Journal = {Journal of Computational Physics},
	Number = {23},
	Pages = {7815--7850},
	Publisher = {Elsevier},
	Title = {Bayesian inference with optimal maps},
	Volume = {231},
	Year = {2012}}

@article{gelman1998simulating,
	Author = {Gelman, Andrew and Meng, Xiao-Li},
	Journal = {Statistical Science},
	Number = {2},
	Pages = {163--185},
	Publisher = {JSTOR},
	Title = {Simulating normalizing constants: From importance sampling to bridge sampling to path sampling},
	Volume = {13},
	Year = {1998}}

@article{jarzynski1997nonequilibrium,
	Author = {Jarzynski, Christopher},
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	Volume = {78},
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@article{marzouk2016introduction,
	Author = {Marzouk, Youssef and Moselhy, Tarek and Parno, Matthew and Spantini, Alessio},
	Journal = {arXiv preprint arXiv:1602.05023},
	Title = {An introduction to sampling via measure transport},
	Year = {2016}}

@article{heng2015gibbs,
	Author = {Heng, Jeremy and Doucet, Arnaud and Pokern, Yvo},
	Journal = {Journal of the Royal Statistical Society Series \textup{B}},
	Title = {Gibbs flow for approximate transport with applications to {B}ayesian computation},
	Volume ={83},
	Number ={1},
	pages={156--187},
	Year = {2021}}

@article{papamakarios2019normalizing,
  title={Normalizing flows for probabilistic modeling and inference},
  author={Papamakarios, George and Nalisnick, Eric and Rezende, Danilo Jimenez and Mohamed, Shakir and Lakshminarayanan, Balaji},
  journal={The Journal of Machine Learning Research},
  volume={22},
  number={1},
  pages={2617--2680},
  year={2021}
}

@article{kappen2016adaptive,
	Author = {Kappen, Hilbert J and Ruiz, Hans Christian},
	Journal = {Journal of Statistical Physics},
	Number = {5},
	Pages = {1244--1266},
	Publisher = {Springer},
	Title = {Adaptive importance sampling for control and inference},
	Volume = {162},
	Year = {2016}}

@article{hartmann2019variational,
	Author = {Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz},
	Journal = {Chaos: An Interdisciplinary Journal of Nonlinear Science},
	Number = {6},
	Pages = {063107},
	Publisher = {AIP Publishing LLC},
	Title = {Variational approach to rare event simulation using least-squares regression},
	Volume = {29},
	Year = {2019}}

@article{sinha2020neural,
	Author = {Sinha, Aman and O'Kelly, Matthew and Duchi, John and Tedrake, Russ},
	Journal = {arXiv preprint arXiv:2008.10581},
	Title = {Neural Bridge Sampling for Evaluating Safety-Critical Autonomous Systems},
	Year = {2020}}


@article{neal2001annealed,
	Author = {Neal, Radford M},
	Journal = {Statistics and Computing},
	Number = {2},
	Pages = {125--139},
	Publisher = {Springer},
	Title = {Annealed importance sampling},
	Volume = {11},
	Year = {2001}}

@article{spantini2018inference,
	Author = {Spantini, Alessio and Bigoni, Daniele and Marzouk, Youssef},
	Journal = {The Journal of Machine Learning Research},
	Number = {1},
	Pages = {2639--2709},
	Publisher = {JMLR. org},
	Title = {Inference via low-dimensional couplings},
	Volume = {19},
	Year = {2018}}

@article{vaikuntanathan2008escorted,
	Author = {Vaikuntanathan, Suriyanarayanan and Jarzynski, Christopher},
	Journal = {Physical Review Letters},
	Number = {19},
	Pages = {190601},
	Publisher = {APS},
	Title = {Escorted free energy simulations: Improving convergence by reducing dissipation},
	Volume = {100},
	Year = {2008}}

@article{vaikuntanathan2011escorted,
	Author = {Vaikuntanathan, Suriyanarayanan and Jarzynski, Christopher},
	Journal = {The Journal of Chemical Physics},
	Number = {5},
	Pages = {054107},
	Publisher = {American Institute of Physics},
	Title = {Escorted free energy simulations},
	Volume = {134},
	Year = {2011}}

@article{everitt2020sequential,
	Author = {Everitt, Richard G and Culliford, Richard and Medina-Aguayo, Felipe and Wilson, Daniel J},
	Journal = {Statistics and Computing},
	Number = {3},
	Pages = {663--676},
	Publisher = {Springer},
	Title = {Sequential {M}onte {C}arlo with transformations},
	Volume = {30},
	Year = {2020}}

@article{jarzynski2002targeted,
	Author = {Jarzynski, C},
	Journal = {Physical Review E},
	Number = {4},
	Pages = {046122},
	Publisher = {APS},
	Title = {Targeted free energy perturbation},
	Volume = {65},
	Year = {2002}}

@article{wirnsberger2020targeted,
	Author = {Wirnsberger, Peter and Ballard, Andrew J and Papamakarios, George and Abercrombie, Stuart and Racani{\`e}re, S{\'e}bastien and Pritzel, Alexander and Rezende, Danilo Jimenez and Blundell, Charles},
	Journal = {arXiv preprint arXiv:2002.04913},
	Title = {Targeted free energy estimation via learned mappings},
	Year = {2020}}

@article{dai2020invitation,
	Author = {Dai, Chenguang and Heng, Jeremy and Jacob, Pierre E and Whiteley, Nick},
	Journal = {arXiv preprint arXiv:2007.11936},
	Title = {An invitation to sequential {M}onte {C}arlo samplers},
	Year = {2020}}

@inproceedings{wunoe2020stochastic,
	Author = {Wu, Hao and K{\"o}hler, Jonas and No{\'e}, Frank},
	booktitle = {Advances in Neural Information Processing Systems},
	Title = {Stochastic Normalizing Flows},
	Year = {2020}}

@article{nilmeier2011nonequilibrium,
	Author = {Nilmeier, Jerome P and Crooks, Gavin E and Minh, David DL and Chodera, John D},
	Journal = {Proceedings of the National Academy of Sciences},
	Number = {45},
	Pages = {E1009--E1018},
	Publisher = {National Acad Sciences},
	Title = {Nonequilibrium candidate {M}onte {C}arlo is an efficient tool for equilibrium simulation},
	Volume = {108},
	Year = {2011}}

@inproceedings{salimans2015markov,
	Author = {Salimans, Tim and Kingma, Diederik and Welling, Max},
	Booktitle = {International Conference on Machine Learning},
	Title = {Markov chain {M}onte {C}arlo and variational inference: Bridging the gap},
	Year = {2015}}

@inproceedings{goyal2017variational,
	Author = {Goyal, Anirudh Goyal Alias Parth and Ke, Nan Rosemary and Ganguli, Surya and Bengio, Yoshua},
	Booktitle = {Advances in Neural Information Processing Systems},
	Pages = {4392--4402},
	Title = {Variational walkback: Learning a transition operator as a stochastic recurrent net},
	Year = {2017}}

@article{crooks1998nonequilibrium,
	Author = {Crooks, Gavin E},
	Journal = {Journal of Statistical Physics},
	Number = {5-6},
	Pages = {1481--1487},
	Publisher = {Springer},
	Title = {Nonequilibrium measurements of free energy differences for microscopically reversible {M}arkovian systems},
	Volume = {90},
	Year = {1998}}

@article{ZhouJohansen2016,
	Author = {Yan Zhou and Adam M. Johansen and John A.D. Aston},
	Journal = {Journal of Computational and Graphical Statistics},
	Number = {3},
	Pages = {701-726},
	Title = {Toward Automatic Model Comparison: An Adaptive Sequential {M}onte {C}arlo Approach},
	Volume = {25},
	Year = {2016}}

@inproceedings{caterini2018hamiltonian,
	Author = {Caterini, Anthony L and Doucet, Arnaud and Sejdinovic, Dino},
	Booktitle = {Advances in Neural Information Processing Systems},
	Pages = {8167--8177},
	Title = {Hamiltonian variational auto-encoder},
	Year = {2018}}

@article{jasra2011inference,
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	Number = {1},
	Pages = {1--22},
	Publisher = {Wiley Online Library},
	Title = {Inference for {L}{\'e}vy-driven stochastic volatility models via adaptive sequential {M}onte {C}arlo},
	Volume = {38},
	Year = {2011}}

@article{swendsen1986replica,
	Author = {Swendsen, Robert H and Wang, Jian-Sheng},
	Journal = {Physical Review Letters},
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@article{marinari1992simulated,
	Author = {Marinari, Enzo and Parisi, Giorgio},
	Journal = {EPL (Europhysics Letters)},
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	Pages = {451},
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@article{liuchen1995,
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  journal={Bernoulli},
  pages={341--363},
  year={1996},
  publisher={JSTOR}
}

@article{grillo1994logarithmic,
  title={Logarithmic {S}obolev inequalities and {L}angevin algorithms in $\mathbb{R}^n$},
  author={Grillo, Gabriele},
  journal={Stochastic Analysis and Applications},
  volume={12},
  number={3},
  pages={309--328},
  year={1994},
  publisher={Taylor \& Francis}
}

%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/

%% Created for Michael N. Arbel at 2021-02-08 16:08:23 +0000 


%% Saved with string encoding Unicode (UTF-8) 
@misc{Rippel2013,
      title={High-Dimensional Probability Estimation with Deep Density Models}, 
      author={Oren Rippel and Ryan Prescott Adams},
      year={2013},
      eprint={1302.5125},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@inproceedings{Dinh2015,
  author    = {Laurent Dinh and
               David Krueger and
               Yoshua Bengio},
  title     = {{NICE:} Non-linear Independent Components Estimation},
  booktitle = {3rd International Conference on Learning Representations, {ICLR}},
  year      = {2015}
}




@inproceedings{Zimmermann:2021,
	Author = {Heiko Zimmermann and Hao Wu and Babak Esmaeili and Jan-Willem van de Meent},
	Booktitle = {Advances in Neural Information Processing Systems},
    Title = {Nested Variational Inference},
	Year = {2021}
}



@InProceedings{Thin:2021,
  title = 	 {Monte {C}arlo Variational Auto-Encoders},
  author =       {Thin, Achille and Kotelevskii, Nikita and Durmus, Alain and Moulines, Eric and Panov, Maxim and Doucet, Arnaud},
  booktitle = 	 {International Conference on Machine Learning},
  year = 	 {2021},
}


@software{optax2020github,
	Author = {Matteo Hessel and David Budden and Fabio Viola and Mihaela Rosca and Eren Sezener and Tom Hennigan},
	Title = {Optax: composable gradient transformation and optimisation, in JAX.},
	Version = {0.0.1},
	Year = {2020}}


@article{Neal:2012,
	Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	Adsurl = {https://ui.adsabs.harvard.edu/abs/2012arXiv1206.1901N},
	Archiveprefix = {arXiv},
	Author = {{Neal}, Radford M.},
	Eid = {arXiv:1206.1901},
	Eprint = {1206.1901},
	Journal = {arXiv e-prints},
	Keywords = {Statistics - Computation, Physics - Computational Physics},
	Month = jun,
	Pages = {arXiv:1206.1901},
	Primaryclass = {stat.CO},
	Title = {{MCMC using Hamiltonian dynamics}},
	Year = 2012}

@article{Beskos:2011,
	Author = {A. Beskos and F.J. Pinski and J.M. Sanz-Serna and A.M. Stuart},
	Issn = {0304-4149},
	Journal = {Stochastic Processes and their Applications},
	Number = {10},
	Pages = {2201 - 2230},
	Title = {Hybrid {M}onte {C}arlo on {H}ilbert spaces},
	Volume = {121},
	Year = {2011},}

@article{lee2010utility,
	Author = {Lee, Anthony and Yau, Christopher and Giles, Michael B and Doucet, Arnaud and Holmes, Chris C},
	Journal = {Journal of Computational and Graphical Statistics},
	Number = {4},
	Pages = {769--789},
	Publisher = {ASA},
	Title = {On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods},
	Volume = {19},
	Year = {2010}}

@inproceedings{Durkan:2019,
	Author = {Durkan, Conor and Bekasov, Artur and Murray, Iain and Papamakarios, George},
	Booktitle = {Advances in Neural Information Processing Systems},
	Title = {Neural Spline Flows},
	Year = {2019},}

@article{Neal:2003,
	Author = {Neal, Radford M.},
	Fjournal = {Annals of Statistics},
	Journal = {The Annals of Statistics},
	Month = {06},
	Pages = {705--767},
	Publisher = {The Institute of Mathematical Statistics},
	Title = {Slice sampling},
	Volume = {31},
	Year = {2003},}

@article{Dillon:2017,
	Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	Author = {{Dillon}, Joshua V. and {Langmore}, Ian and {Tran}, Dustin and {Brevdo}, Eugene and {Vasudevan}, Srinivas and {Moore}, Dave and {Patton}, Brian and {Alemi}, Alex and {Hoffman}, Matt and {Saurous}, Rif A.},
	Journal = {arXiv preprint arXiv:1711.10604},
	Title = {{TensorFlow Distributions}},
	Year = 2017}

@software{Hennigan:2020,
	Author = {Tom Hennigan and Trevor Cai and Tamara Norman and Igor Babuschkin},
	Title = {{H}aiku: {S}onnet for {JAX}},
	Version = {0.0.3},
	Year = {2020},}

@software{Bradbury:2018,
	Author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang},
	Title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs},
	Version = {0.2.5},
	Year = {2018},}

@article{Moller:1998,
	Author = {Jesper M{\o}ller and Anne Randi Syversveen and Rasmus Plenge Waagepetersen},
	Journal = {Scandinavian Journal of Statistics},
	Number = {3},
	Pages = {451--482},
	Title = {Log {G}aussian {C}ox Processes},
	Volume = {25},
	Year = {1998}}

@article{Hoffman:2014,
	Author = {Matthew D. Hoffman and Andrew Gelman},
	Journal = {Journal of Machine Learning Research},
	Number = {47},
	Pages = {1593-1623},
	Title = {The {N}o-{U}-{T}urn {S}ampler: Adaptively Setting Path Lengths in {H}amiltonian Monte Carlo},
	Url = {http://jmlr.org/papers/v15/hoffman14a.html},
	Volume = {15},
	Year = {2014}}

@inproceedings{Kingma:2014,
  author =        {Diederik P. Kingma and Jimmy Ba},
  booktitle =     {International Conference on Learning
                   Representations},
  title =         {Adam: {A} Method for Stochastic Optimization},
  year =          {2015},
}

@article{Behr:2018,
	Annote = {Comment: 30 pages, 51 figures},
	Author = {Behr, Maximilian and Benner, Peter and Heiland, Jan},
	Journal = {arXiv:1811.08327 [math]},
	Keywords = {15A24, 65F60, 65L05, Mathematics - Numerical Analysis},
	Month = nov,
	Note = {arXiv: 1811.08327},
	Title = {Solution {Formulas} for {Differential} {Sylvester} and {Lyapunov} {Equations}},
	Url = {http://arxiv.org/abs/1811.08327},
	Urldate = {2019-10-24},
	Year = {2018}}

@article{Carrillo:2006,
	Abstract = {An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) --- if uniformly controlled --- will quantify contractivity (limit expansivity) of the flow.},
	Author = {Carrillo, Jos{\'e} A. and McCann, Robert J. and Villani, C{\'e}dric},
	Date-Added = {2019-07-27 15:18:39 +0000},
	Date-Modified = {2019-07-27 15:18:39 +0000},
	Doi = {10.1007/s00205-005-0386-1},
	Issn = {1432-0673},
	Journal = {Archive for Rational Mechanics and Analysis},
	Keywords = {Complex System, Decay Rate, Manifold, Neural Network, Nonlinear Dynamics},
	Language = {en},
	Month = feb,
	Number = {2},
	Pages = {217--263},
	Title = {Contractions in the 2-{Wasserstein} {Length} {Space} and {Thermalization} of {Granular} {Media}},
	Url = {https://doi.org/10.1007/s00205-005-0386-1},
	Urldate = {2019-07-27},
	Volume = {179},
	Year = {2006},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00205-005-0386-1}}

@article{kondratyev2016new,
	Author = {Kondratyev, Stanislav and Monsaingeon, L{\'e}onard and Vorotnikov, Dmitry and others},
	Journal = {Advances in Differential Equations},
	Title = {A new optimal transport distance on the space of finite Radon measures},
	Year = {2016}}

@article{liero2016optimal,
	Author = {Liero, Matthias and Mielke, Alexander and Savar{\'e}, Giuseppe},
	Journal = {SIAM Journal on Mathematical Analysis},
	Title = {Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves},
	Year = {2016}}

@article{Chizat:2015,
	Author = {Chizat, Lenaic and Schmitzer, Bernhard and Peyr{\'e}, Gabriel and Vialard, Fran{\c c}ois-Xavier},
	Journal = {arXiv:1506.06430 [math]},
	Title = {An {Interpolating} {Distance} between {Optimal} {Transport} and {Fisher}-{Rao}},
	Url = {http://arxiv.org/abs/1506.06430},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1506.06430}}

@article{Shestakov:2009,
	Author = {Shestakov, Ivan V. and Shlapunov, Alexander A.},
	Date-Added = {2019-06-10 23:02:02 +0000},
	Date-Modified = {2019-06-10 23:02:02 +0000},
	Language = {en},
	Month = jan,
	Title = {Negative {Sobolev} {Spaces} in the {Cauchy} {Problem} for the {Cauchy}-{Riemann} {Operator}},
	Url = {http://elib.sfu-kras.ru/handle/2311/877},
	Urldate = {2019-06-10},
	Year = {2009},
	Bdsk-Url-1 = {http://elib.sfu-kras.ru/handle/2311/877}}

@article{Chizat:2018a,
	Author = {Chizat, Lenaic and Bach, Francis},
	Journal = {arXiv:1812.07956 [cs, math]},
	Month = dec,
	Note = {arXiv: 1812.07956},
	Title = {A {Note} on {Lazy} {Training} in {Supervised} {Differentiable} {Programming}},
	Url = {http://arxiv.org/abs/1812.07956},
	Urldate = {2019-05-05},
	Year = {2018},
	Bdsk-Url-1 = {http://arxiv.org/abs/1812.07956}}

@book{Villani:2003,
	Author = {Villani, Cedric},
	Date-Added = {2019-05-23 19:24:39 +0000},
	Date-Modified = {2019-05-23 19:24:40 +0000},
	Isbn = {978-0-8218-3312-4},
	Keywords = {Mathematics / General},
	Language = {en},
	Publisher = {American Mathematical Soc.},
	Title = {Topics in {Optimal} {Transportation}},
	Year = {2003}}

@article{dalalyan2019user,
	Author = {Dalalyan, Arnak S and Karagulyan, Avetik},
	Journal = {Stochastic Processes and their Applications},
	Publisher = {Elsevier},
	Title = {User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient},
	Year = {2019}}

@article{benamou2000computational,
	Author = {Benamou, Jean-David and Brenier, Yann},
	Journal = {Numerische Mathematik},
	Number = {3},
	Pages = {375--393},
	Publisher = {Springer},
	Title = {A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem},
	Volume = {84},
	Year = {2000}}

@article{oguntuase2001inequality,
	Author = {Oguntuase, James Adedayo},
	Journal = {Journal of Inequalities in Pure and Applied Mathematics},
	Title = {On an inequality of Gronwall},
	Year = {2001}}

@article{carrillo2006contractions,
	Author = {Carrillo, Jos{\'e} A and McCann, Robert J and Villani, C{\'e}dric},
	Journal = {Archive for Rational Mechanics and Analysis},
	Number = {2},
	Pages = {217--263},
	Publisher = {Springer},
	Title = {Contractions in the 2-Wasserstein length space and thermalization of granular media},
	Volume = {179},
	Year = {2006}}

@article{Sirignano:2018,
	Abstract = {Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also growing applications in engineering, robotics, medicine, and finance. Despite their immense success in practice, there is limited mathematical understanding of neural networks. This paper illustrates how neural networks can be studied via stochastic analysis, and develops approaches for addressing some of the technical challenges which arise. We analyze one-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously prove that the empirical distribution of the neural network parameters converges to the solution of a nonlinear partial differential equation. This result can be considered a law of large numbers for neural networks. In addition, a consequence of our analysis is that the trained parameters of the neural network asymptotically become independent, a property which is commonly called "propagation of chaos".},
	Author = {Sirignano, Justin and Spiliopoulos, Konstantinos},
	Date-Added = {2019-05-21 23:57:16 +0000},
	Date-Modified = {2019-05-21 23:57:16 +0000},
	Journal = {arXiv:1805.01053 [math]},
	Keywords = {Mathematics - Probability},
	Month = may,
	Note = {arXiv: 1805.01053},
	Title = {Mean {Field} {Analysis} of {Neural} {Networks}},
	Url = {http://arxiv.org/abs/1805.01053},
	Urldate = {2019-05-21},
	Year = {2018},
	Bdsk-Url-1 = {http://arxiv.org/abs/1805.01053}}

@article{Dziugaite:2015a,
	Abstract = {We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. As our two-sample test statistic, we use an unbiased estimate of the maximum mean discrepancy, which is the centerpiece of the nonparametric kernel two-sample test proposed by Gretton et al. (2012). We compare to the adversarial nets framework introduced by Goodfellow et al. (2014), in which learning is a two-player game between a generator network and an adversarial discriminator network, both trained to outwit the other. From this perspective, the MMD statistic plays the role of the discriminator. In addition to empirical comparisons, we prove bounds on the generalization error incurred by optimizing the empirical MMD.},
	Annote = {Comment: 10 pages, to appear in Uncertainty in Artificial Intelligence (UAI) 2015},
	Author = {Dziugaite, Gintare Karolina and Roy, Daniel M. and Ghahramani, Zoubin},
	Date-Added = {2019-05-21 23:56:45 +0000},
	Date-Modified = {2019-05-21 23:56:45 +0000},
	Journal = {arXiv:1505.03906 [cs, stat]},
	Keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
	Month = may,
	Note = {arXiv: 1505.03906},
	Title = {Training generative neural networks via {Maximum} {Mean} {Discrepancy} optimization},
	Url = {http://arxiv.org/abs/1505.03906},
	Urldate = {2019-05-21},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1505.03906}}

@article{Uppal:2019,
	Author = {Uppal, Ananya and Singh, Shashank and P{\'o}czos, Barna{\'a}s},
	Journal = {arXiv preprint arXiv:1902.03511},
	Title = {Nonparametric Density Estimation under Besov IPM Losses},
	Year = {2019}}

@article{Li:2015,
	Author = {Li, Yujia and Swersky, Kevin and Zemel, Richard},
	Journal = {arXiv preprint arXiv:1502.02761},
	Title = {Generative moment matching networks},
	Year = {2015}}

@article{Li:2017a,
	Abstract = {Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing adversarial kernel learning techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD GAN. The new distance measure in MMD GAN is a meaningful loss that enjoys the advantage of weak topology and can be optimized via gradient descent with relatively small batch sizes. In our evaluation on multiple benchmark datasets, including MNIST, CIFAR- 10, CelebA and LSUN, the performance of MMD-GAN significantly outperforms GMMN, and is competitive with other representative GAN works.},
	Annote = {Comment: In the Proceedings of Thirty-first Annual Conference on Neural Information Processing Systems (NIPS 2017)},
	Author = {Li, Chun-Liang and Chang, Wei-Cheng and Cheng, Yu and Yang, Yiming and P{\'o}czos, Barnab{\'a}s},
	Date-Added = {2019-05-21 16:17:09 +0000},
	Date-Modified = {2019-05-21 16:17:09 +0000},
	Journal = {arXiv:1705.08584 [cs, stat]},
	Keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
	Month = may,
	Note = {arXiv: 1705.08584},
	Shorttitle = {{MMD} {GAN}},
	Title = {{MMD} {GAN}: {Towards} {Deeper} {Understanding} of {Moment} {Matching} {Network}},
	Url = {http://arxiv.org/abs/1705.08584},
	Urldate = {2018-11-13},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1705.08584}}

@article{Bolte:2016,
	Author = {Blanchet, Adrien and Bolte, J{\'e}r{\^o}me},
	Journal = {Journal of Functional Analysis},
	Number = {7},
	Pages = {1650--1673},
	Publisher = {Elsevier},
	Title = {A family of functional inequalities: {\L}ojasiewicz inequalities and displacement convex functions},
	Volume = {275},
	Year = {2018}}

@book{Steinwart:2008a,
	Author = {Steinwart, Ingo and Christmann, Andreas},
	Date-Added = {2019-05-19 11:35:35 +0000},
	Date-Modified = {2019-05-19 11:35:35 +0000},
	Edition = {1st},
	Isbn = {0387772413},
	Publisher = {Springer Publishing Company, Incorporated},
	Title = {Support Vector Machines},
	Year = {2008}}

@inproceedings{Mroueh:2019,
	Author = {Mroueh, Youssef and Sercu, Tom and Raj, Anant},
	Booktitle = {AISTATS},
	Title = {Sobolev Descent},
	Year = {2019}}

@article{Peyre:2011,
	Author = {Peyre, R{\'e}mi},
	Journal = {ESAIM: Control, Optimisation and Calculus of Variations},
	Number = {4},
	Pages = {1489--1501},
	Publisher = {EDP Sciences},
	Title = {Comparison between {$W_2$} distance and {$\dot{H}^{-1}$} norm, and localisation of {Wasserstein} distance},
	Volume = {24},
	Year = {2018}}

@article{Otto:2000,
	Author = {Otto, Felix and Villani, C{\'e}dric},
	Journal = {Journal of Functional Analysis},
	Number = {2},
	Pages = {361--400},
	Publisher = {Elsevier},
	Title = {Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality},
	Volume = {173},
	Year = {2000}}

@article{carrillo2019blob,
	Author = {Carrillo, Jos{\'e} Antonio and Craig, Katy and Patacchini, Francesco S},
	Date-Added = {2019-05-17 17:13:25 +0000},
	Date-Modified = {2019-05-17 17:13:25 +0000},
	Journal = {Calculus of Variations and Partial Differential Equations},
	Number = {2},
	Pages = {53},
	Publisher = {Springer},
	Title = {A blob method for diffusion},
	Volume = {58},
	Year = {2019}}

@article{craig2016blob,
	Author = {Craig, Katy and Bertozzi, Andrea},
	Date-Added = {2019-05-17 17:13:11 +0000},
	Date-Modified = {2019-05-17 17:13:11 +0000},
	Journal = {Mathematics of computation},
	Number = {300},
	Pages = {1681--1717},
	Title = {A blob method for the aggregation equation},
	Volume = {85},
	Year = {2016}}

@article{Chaudhari:2017,
	Author = {Chaudhari, Pratik and Oberman, Adam and Osher, Stanley and Soatto, Stefano and Carlier, Guillaume},
	Journal = {arXiv:1704.04932 [cs, math]},
	Title = {Deep {Relaxation}: partial differential equations for optimizing deep neural networks},
	Url = {http://arxiv.org/abs/1704.04932},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1704.04932}}

@inproceedings{Hazan:2015,
	Author = {Hazan, Elad and Levy, Kfir Yehuda and Shalev-Shwartz, Shai},
	Booktitle = {ICML},
	Title = {On graduated optimization for stochastic non-convex problems},
	Year = {2016}}

@article{Gulcehre:2016,
	Author = {Gulcehre, Caglar and Moczulski, Marcin and Visin, Francesco and Bengio, Yoshua},
	Journal = {arXiv preprint arXiv:1608.04980},
	Title = {Mollifying networks},
	Year = {2016}}

@article{Mobahi:2016,
	Abstract = {This work presents a new algorithm for training recurrent neural networks (although ideas are applicable to feedforward networks as well). The algorithm is derived from a theory in nonconvex optimization related to the diffusion equation. The contributions made in this work are two fold. First, we show how some seemingly disconnected mechanisms used in deep learning such as smart initialization, annealed learning rate, layerwise pretraining, and noise injection (as done in dropout and SGD) arise naturally and automatically from this framework, without manually crafting them into the algorithms. Second, we present some preliminary results on comparing the proposed method against SGD. It turns out that the new algorithm can achieve similar level of generalization accuracy of SGD in much fewer number of epochs.},
	Author = {Mobahi, Hossein},
	Date-Added = {2019-05-17 16:53:44 +0000},
	Date-Modified = {2019-05-17 16:53:44 +0000},
	Journal = {arXiv:1601.04114 [cs]},
	Keywords = {Computer Science - Machine Learning},
	Month = jan,
	Note = {arXiv: 1601.04114},
	Title = {Training {Recurrent} {Neural} {Networks} by {Diffusion}},
	Url = {http://arxiv.org/abs/1601.04114},
	Urldate = {2019-05-17},
	Year = {2016},
	Bdsk-Url-1 = {http://arxiv.org/abs/1601.04114}}

@inproceedings{Gulcehre:2016a,
	Author = {Gulcehre, Caglar and Moczulski, Marcin and Denil, Misha and Bengio, Yoshua},
	Booktitle = {ICML},
	Title = {Noisy activation functions},
	Year = {2016}}

@article{tolstikhin2017minimax,
	Author = {Tolstikhin, Ilya and Sriperumbudur, Bharath K and Muandet, Krikamol},
	Journal = {The Journal of Machine Learning Research},
	Number = {1},
	Pages = {3002--3048},
	Publisher = {JMLR. org},
	Title = {Minimax estimation of kernel mean embeddings},
	Volume = {18},
	Year = {2017}}

@article{herrmann2010non,
	Author = {Herrmann, Samuel and Tugaut, Julian},
	Journal = {Stochastic Processes and their Applications},
	Number = {7},
	Pages = {1215--1246},
	Publisher = {Elsevier},
	Title = {Non-uniqueness of stationary measures for self-stabilizing processes},
	Volume = {120},
	Year = {2010}}

@article{tugaut2014phase,
	Author = {Tugaut, Julian},
	Journal = {Stochastics An International Journal of Probability and Stochastic Processes},
	Number = {2},
	Pages = {257--284},
	Publisher = {Taylor \& Francis},
	Title = {Phase transitions of McKean--Vlasov processes in double-wells landscape},
	Volume = {86},
	Year = {2014}}

@article{tugaut2013convergence,
	Author = {Tugaut, Julian and others},
	Journal = {The Annals of Probability},
	Number = {3A},
	Pages = {1427--1460},
	Publisher = {Institute of Mathematical Statistics},
	Title = {Convergence to the equilibria for self-stabilizing processes in double-well landscape},
	Volume = {41},
	Year = {2013}}

@article{tugaut2014self,
	Author = {Tugaut, Julian},
	Journal = {Journal of Theoretical Probability},
	Number = {1},
	Pages = {57--79},
	Publisher = {Springer},
	Title = {Self-stabilizing Processes in Multi-wells Landscape in $\mathbb{R}^d$-Invariant Probabilities},
	Volume = {27},
	Year = {2014}}

@article{sutherland2017efficient,
	Author = {Sutherland, Dougal J and Strathmann, Heiko and Arbel, Michael and Gretton, Arthur},
	Journal = {AISTATS},
	Title = {Efficient and principled score estimation with Nystr{\"o}m kernel exponential families},
	Year = {2018}}

@inproceedings{csimcsekli2018sliced,
	Author = {{\c{S}}im{\c{s}}ekli, Umut and Liutkus, Antoine and Majewski, Szymon and Durmus, Alain},
	Booktitle = {ICML},
	Title = {Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions},
	Year = {2019}}

@article{rotskoff2018neural,
	Author = {Rotskoff, Grant M and Vanden-Eijnden, Eric},
	Journal = {arXiv preprint arXiv:1805.00915},
	Title = {Neural networks as interacting particle systems: Asymptotic convexity of the loss landscape and universal scaling of the approximation error},
	Year = {2018}}

@article{mei2018mean,
	Author = {Mei, Song and Montanari, Andrea and Nguyen, Phan-Minh},
	Journal = {Proceedings of the National Academy of Sciences},
	Number = {33},
	Pages = {E7665--E7671},
	Publisher = {National Acad Sciences},
	Title = {A mean field view of the landscape of two-layer neural networks},
	Volume = {115},
	Year = {2018}}

@article{sirignano2018mean,
	Author = {Sirignano, Justin and Spiliopoulos, Konstantinos},
	Journal = {arXiv preprint arXiv:1808.09372},
	Title = {Mean field analysis of neural networks: A central limit theorem},
	Year = {2018}}

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@inproceedings{kernel-choice-mmd,
	Author = {Sriperumbudur, B. K. and Fukumizu, K. and Gretton, A. and Lanckriet, G. R. G. and Sch{\"{o}}lkopf, B.},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Kernel choice and classifiability for {RKHS} embeddings of probability distributions},
	Year = {2009}}

@book{shawe-taylor-christianini,
	Author = {Shawe-Taylor, John and Cristianini, Nello},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Publisher = {Cambridge University Press},
	Title = {Kernel Methods for Pattern Analysis},
	Year = {2004}}

@inproceedings{sinkhorn-igm,
	Archiveprefix = {arXiv},
	Author = {Aude Genevay and Gabriel Peyr{\'e} and Marco Cuturi},
	Booktitle = {AISTATS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1706.00292},
	Title = {Learning Generative Models with {S}inkhorn Divergences},
	Year = {2018}}

@misc{igms,
	Archiveprefix = {arXiv},
	Author = {Mohamed, Shakir and Lakshminarayanan, Balaji},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1610.03483},
	Title = {Learning in Implicit Generative Models},
	Year = {2016}}

@misc{cifar10,
	Author = {Krizhevsky, A.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Learning Multiple Layers of Features from Tiny Images},
	Year = {2009}}

@misc{lsun,
	Archiveprefix = {arXiv},
	Author = {Yu, F. and Zhang, Y. and Song, S. and Seff, A. and Xiao, J.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1506.03365},
	Title = {{LSUN}: Construction of a Large-scale Image Dataset using Deep Learning with Humans in the Loop},
	Year = {2015}}

@inproceedings{many-paths,
	Archiveprefix = {arXiv},
	Author = {W. Fedus and M. Rosca and B. Lakshminarayanan and A. M. Dai and S. Mohamed and I. Goodfellow},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1710.08446},
	Title = {Many Paths to Equilibrium: {GAN}s Do Not Need to Decrease a Divergence At Every Step},
	Year = {2018}}

@inproceedings{mcgan,
	Archiveprefix = {arXiv},
	Author = {Mroueh, Youssef and Sercu, Tom and Goel, V.},
	Booktitle = {ICML},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1702.08398},
	Title = {{McGan}: Mean and Covariance Feature Matching {GAN}},
	Year = {2017}}

@incollection{Bousquet:2004,
	Author = {Bousquet, Olivier and Chapelle, Olivier and Hein, Matthias},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Measure Based Regularization},
	Year = {2004}}

@inproceedings{mmd-gan,
	Author = {Li, Chun-Liang and Chang, Wei-Cheng and Cheng, Yu and Yang, Yiming and P{\'o}czos, Barnab{\'a}s},
	Booktitle = {NIPS},
	Title = {Mmd gan: Towards deeper understanding of moment matching network},
	Year = {2017}}

@misc{mnist,
	Author = {LeCun, Yann and Cortes, Corinna},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Howpublished = {http://yann.lecun.com/exdb/mnist/},
	Title = {{MNIST} handwritten digit database},
	Url = {http://yann.lecun.com/exdb/mnist/},
	Year = {2010},
	Bdsk-Url-1 = {http://yann.lecun.com/exdb/mnist/}}

@article{rosenbaum,
	Author = {Rosenbaum, S.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {JRSS B},
	Pages = {405--408},
	Title = {Moments of a Truncated Bivariate Normal Distribution},
	Volume = {23},
	Year = {1961}}

@misc{munit,
	Archiveprefix = {arXiv},
	Arxivid = {1804.04732},
	Author = {Huang, Xun and Liu, Ming-Yu and Belongie, Serge and Kautz, Jan},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1804.04732},
	Title = {Multimodal Unsupervised Image-to-Image Translation},
	Year = {2018}}

@article{Brock:2016,
	Author = {Brock, Andrew and Lim, Theodore and Ritchie, J. M. and Weston, Nick},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Language = {en},
	Month = sep,
	Title = {Neural {Photo} {Editing} with {Introspective} {Adversarial} {Networks}},
	Url = {https://arxiv.org/abs/1609.07093},
	Urldate = {2018-06-19},
	Year = {2016},
	Bdsk-Url-1 = {https://arxiv.org/abs/1609.07093}}

@article{gan-tutorial,
	Archiveprefix = {arXiv},
	Author = {Goodfellow, I.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1701.00160},
	Title = {{NIPS} 2016 Tutorial: Generative Adversarial Networks},
	Year = {2016}}

@misc{ipms-phi-clf,
	Archiveprefix = {arXiv},
	Author = {Sriperumbudur, B. K. and Fukumizu, K. and Gretton, A. and Sch{\"{o}}lkopf, B. and Lanckriet, G. R. G.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {0901.2698},
	Title = {On integral probability metrics, phi-divergences and binary classification},
	Year = {2009}}

@article{ipm-empirical-est,
	Author = {Sriperumbudur, B. K. and Fukumizu, K. and Gretton, A. and Sch{\"{o}}lkopf, B. and Lanckriet, G. R. G.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Electronic Journal of Statistics},
	Pages = {1550--1599},
	Title = {On the empirical estimation of integral probability metrics},
	Volume = {6},
	Year = {2012}}

@article{opt-est-probabilities,
	Archiveprefix = {arXiv},
	Author = {Sriperumbudur, Bharath},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1310.8240},
	Journal = {Bernoulli},
	Number = {3},
	Pages = {1839--1893},
	Title = {On the optimal estimation of probability mesaures in weak and strong topologies},
	Volume = {22},
	Year = {2016}}

@mastersthesis{energy-distance-gan,
	Author = {L. Liu},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Month = {April},
	School = {University of Princeton Senior Thesis},
	Title = {On the Two-Sample Statistic Approach to Generative Adversarial Networks},
	Url = {http://arks.princeton.edu/ark:/88435/dsp0179408079v},
	Year = {2017},
	Bdsk-Url-1 = {http://arks.princeton.edu/ark:/88435/dsp0179408079v}}

@incollection{Gretton:2012,
	Author = {Gretton, Arthur and Sejdinovic, Dino and Strathmann, Heiko and Balakrishnan, Sivaraman and Pontil, Massimiliano and Fukumizu, Kenji and Sriperumbudur, Bharath K.},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Optimal kernel choice for large-scale two-sample tests},
	Year = {2012}}

@book{Klenke:2008,
	Author = {Klenke, A.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Publisher = {World Publishing Corporation},
	Title = {Probability Theory: A Comprehensive Course},
	Year = {2008}}

@inproceedings{progressive-growing,
	Archiveprefix = {arXiv},
	Arxivid = {1710.10196},
	Author = {Karras, Tero and Aila, Timo and Laine, Samuli and Lehtinen, Jaakko},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1710.10196},
	Title = {Progressive Growing of {GAN}s for Improved Quality, Stability, and Variation},
	Year = {2018}}

@book{dudley:analysis,
	Author = {Richard M. Dudley},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Edition = {2},
	Publisher = {Cambridge University Press},
	Title = {Real Analysis and Probability},
	Year = {2002}}

@inproceedings{inception,
	Archiveprefix = {arXiv},
	Author = {Szegedy, C. and Vanhoucke, V. and Ioffe, S. and Shlens, J. and Wojna, Z.},
	Booktitle = {CVPR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1512.00567},
	Title = {Rethinking the {I}nception Architecture for Computer Vision},
	Year = {2016}}

@inproceedings{c2st,
	Archiveprefix = {arXiv},
	Author = {Lopez-Paz, D. and Oquab, M.},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1610.06545},
	Title = {Revisiting Classifier Two-Sample Tests},
	Year = {2017}}

@book{Wendland05,
	Address = {Cambridge, UK},
	Author = {H. Wendland},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Publisher = {Cambridge University Press},
	Title = {Scattered Data Approximation},
	Year = {2005}}

@article{scikit-learn,
	Author = {Pedregosa, F. and Varoquaux, G. and Gramfort, A. and Michel, V. and Thirion, B. and Grisel, O. and Blondel, M. and Prettenhofer, P. and Weiss, R. and Dubourg, V. and Vanderplas, J. and Passos, A. and Cournapeau, D. and Brucher, M. and Perrot, M. and Duchesnay, E.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {JMLR},
	Pages = {2825--2830},
	Title = {Scikit-learn: Machine Learning in {P}ython},
	Volume = {12},
	Year = {2011}}

@misc{weed:wasserstein-rates,
	Archiveprefix = {arXiv},
	Author = {Jonathan Weed and Francis Bach},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1707.00087},
	Title = {Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance},
	Year = {2017}}

@misc{sobolev-descent,
	Author = {Mroueh, Youssef and Sercu, Tom and Raj, Anant},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Month = 4,
	Note = {Private communication},
	Title = {Sobolev Descent: Variational Transport of Distributions via Advection},
	Year = {2018}}

@inproceedings{sobolev-gan,
	Author = {Mroueh, Youssef and Li, Chung-Liang and Sercu, Tom and Raj, Anant and Cheng, Yu},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Sobolev GAN},
	Year = {2018}}

@inproceedings{Miyato:2018,
	Archiveprefix = {arXiv},
	Author = {Miyato, Takeru and Kataoka, Toshiki and Koyama, Masanori and Yoshida, Yuichi},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1802.05927},
	Title = {Spectral Normalization for Generative Adversarial Networks},
	Year = {2018}}

@inproceedings{roth:regularization,
	Archiveprefix = {arXiv},
	Author = {Roth, Kevin and Lucchi, Aurelien and Nowozin, Sebastian and Hofmann, Thomas},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1705.09367},
	Title = {Stabilizing Training of Generative Adversarial Networks through Regularization},
	Year = {2017}}

@inproceedings{stacked-gans,
	Archiveprefix = {arXiv},
	Author = {Huang, X. and Li, Y. and Poursaeed, O. and Hopcroft, J. and Belongie, S.},
	Booktitle = {CVPR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1612.04357},
	Title = {Stacked Generative Adversarial Networks},
	Year = {2017}}

@article{GneRaf07,
	Author = {T. Gneiting and A. E. Raftery},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {JASA},
	Number = {477},
	Pages = {359--378},
	Title = {Strictly proper scoring rules, prediction, and estimation},
	Volume = {102},
	Year = {2007}}

@book{SteChr08,
	Author = {I. Steinwart and A. Christmann},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Publisher = {Springer},
	Series = {Information Science and Statistics},
	Title = {Support Vector Machines},
	Year = {2008}}

@article{Zahorski:1946,
	Author = {Zahorski, Z.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Bulletin de la Soci{\'e}t{\'e} math{\'e}matique de France},
	Pages = {147--178},
	Title = {Sur l'ensemble des points de non-d{\'e}rivabilit{\'e} d'une fonction continue},
	Urldate = {2018-03-13},
	Volume = {2},
	Year = {1946}}

@article{SzeRiz04,
	Author = {G. Sz\'{e}kely and M. Rizzo},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {InterStat},
	Title = {Testing for Equal Distributions in High Dimension},
	Volume = {5},
	Year = {2004}}

@article{energy-distance,
	Author = {G. J. Sz{\'e}kely and M. L. Rizzo},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {InterStat},
	Number = {5},
	Title = {Testing for equal distributions in high dimensions},
	Year = {2004}}

@inproceedings{kfda,
	Archiveprefix = {arXiv},
	Author = {Harchaoui, Zaid and Bach, Francis R. and Moulines, \'Eric},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {0804.1026},
	Title = {Testing for Homogeneity with Kernel Fisher Discriminant Analysis},
	Year = {2008}}

@misc{cramer-gan,
	Archiveprefix = {arXiv},
	Author = {Bellemare, M. G. and Danihelka, I. and Dabney, W. and Mohamed, S. and Lakshminarayanan, B. and Hoyer, S. and Munos, R.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1705.10743},
	Title = {The {C}ramer Distance as a Solution to Biased {W}asserstein Gradients},
	Year = {2017}}

@article{dowson-landau,
	Author = {Dowson, D. C. and Landau, B. V.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Journal of Multivariate Analysis},
	Number = {3},
	Pages = {450--455},
	Title = {The {F}r{\'{e}}chet distance between multivariate normal distributions},
	Volume = {12},
	Year = {1982}}

@article{Piranian:1966,
	Author = {Piranian, G.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {The American Mathematical Monthly},
	Number = {4},
	Pages = {57--61},
	Title = {The {Set} of {Nondifferentiability} of a {Continuous} {Function}},
	Volume = {73},
	Year = {1966}}

@inproceedings{Zhang:2018,
	Archiveprefix = {arXiv},
	Author = {Zhang, Richard and Isola, Phillip and Efros, Alexei A. and Shechtman, Eli and Wang, Oliver},
	Booktitle = {CVPR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1801.03924},
	Title = {The Unreasonable Effectiveness of Deep Features as a Perceptual Metric},
	Year = {2018}}

@misc{Mityagin:2015,
	Archiveprefix = {arXiv},
	Author = {B. Mityagin},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1512.07276},
	Title = {The Zero Set of a Real Analytic Function},
	Year = {2015}}

@inproceedings{towards-principled-gans,
	Archiveprefix = {arXiv},
	Author = {Arjovsky, M. and Bottou, L.},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1701.04862},
	Title = {Towards Principled Methods for Training Generative Adversarial Networks},
	Year = {2017}}

@misc{anime-gans,
	Archiveprefix = {arXiv},
	Author = {Y. Jin and K. Zhang and M. Li and Y. Tian and H. Zhu and Z. Fang},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1708.05509},
	Title = {Towards the Automatic Anime Characters Creation with Generative Adversarial Networks},
	Year = {2017}}

@inproceedings{gen-mmd,
	Author = {Dziugaite, G. K. and Roy, D. M. and Ghahramani, Z.},
	Booktitle = {UAI},
	Title = {Training generative neural networks via Maximum Mean Discrepancy optimization},
	Year = {2015}}

@article{unbiased-convex,
	Author = {Bickel, P. J. and Lehmann, E. L.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {The Annals of Mathematical Statistics},
	Number = {5},
	Pages = {1523--1535},
	Title = {Unbiased Estimation in Convex Families},
	Volume = {40},
	Year = {1969}}

@article{SriFukLan11,
	Archiveprefix = {arXiv},
	Author = {B. K. Sriperumbudur and K. Fukumizu and G. R. G. Lanckriet},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1003.0887},
	Journal = {JMLR},
	Pages = {2389--2410},
	Title = {Universality, Characteristic Kernels and {RKHS} Embedding of Measures},
	Volume = {12},
	Year = {2011}}

@inproceedings{cyclegan,
	Archiveprefix = {arXiv},
	Author = {J.-Y. Zhu and T. Park and P. Isola and A. A. Efros},
	Booktitle = {ICCV},
	Eprint = {1703.10593},
	Title = {Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks},
	Year = {2017}}

@inproceedings{dcgan,
	Archiveprefix = {arXiv},
	Author = {Radford, A. and Metz, L. and Chintala, S.},
	Booktitle = {ICLR},
	Eprint = {1511.06434},
	Title = {Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks},
	Year = {2016}}

@book{diestel-uhl,
	Address = {Providence},
	Author = {Diestel, J. and Uhl, Jr, J. J.},
	Publisher = {American Mathematical Society},
	Title = {Vector Measures},
	Year = {1977}}

@inproceedings{wgan,
	Archiveprefix = {arXiv},
	Author = {Arjovsky, M. and Chintala, S. and Bottou, L.},
	Booktitle = {ICML},
	Eprint = {1701.07875},
	Title = {{W}asserstein Generative Adversarial Networks},
	Year = {2017}}

@misc{censored-normal,
	Author = {Sutherland, D. J.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Howpublished = {Cross Validated answer},
	Title = {What are the mean and variance of a 0-censored multivariate normal?},
	Url = {https://stats.stackexchange.com/q/326347},
	Year = {2018},
	Bdsk-Url-1 = {https://stats.stackexchange.com/q/326347}}

@misc{Mescheder:2018,
	Archiveprefix = {arXiv},
	Author = {Mescheder, Lars and Geiger, Andreas and Nowozin, Sebastian},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1801.04406},
	Title = {Which Training Methods for {GANs} do actually Converge?},
	Year = {2018}}

@article{Villani:2004,
	Author = {Villani, Cedric},
	Journal = {Contemporary Mathematics},
	Pages = {95},
	Publisher = {Providence, RI: American Mathematical Society},
	Title = {Trend to equilibrium for dissipative equations, functional inequalities and mass transportation},
	Volume = {353},
	Year = {2004}}

@book{Villani:2009,
	Author = {Villani, C{\'e}dric},
	Publisher = {Springer Science \& Business Media},
	Title = {Optimal transport: old and new},
	Volume = {338},
	Year = {2008}}

@article{Oberman:2008,
	Author = {Adam M. Oberman},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Proceedings of the American Mathematical Society},
	Title = {An Explicit Solution of the Lipschitz Extension Problem},
	Year = {2008}}

@article{Saidi:2009,
	Abstract = {Let \$G\$ be a compact subgroup of \$GL\_n({\textbackslash}R)\$ acting linearly on a finite dimensional vector space \$E\$. B. Malgrange has shown that the space \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty({\textbackslash}R{\textasciicircum}n,E){\textasciicircum}G\$ of \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty\$ and \$G\$-covariant functions is a finite module over the ring \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty({\textbackslash}R{\textasciicircum}n){\textasciicircum}G\$ of \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty\$ and \$G\$-invariant functions. First, we generalize this result for the Schwartz space \${\textbackslash}mathscr\{S\}({\textbackslash}R{\textasciicircum}n,E){\textasciicircum}G\$ of \$G\$-covariant functions. Secondly, we prove that any \$G\$-covariant distribution can be decomposed into a sum of \$G\$-invariant distributions multiplied with a fixed family of \$G\$-covariant polynomials. This gives a generalization of an Oksak result proved in ([O]).},
	Author = {Saidi, Anouar},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {arXiv:0902.1383 [math]},
	Keywords = {46F05, 58C46., 58C81, 58C99, Mathematics - Representation Theory},
	Month = feb,
	Note = {arXiv: 0902.1383},
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	Author = {Naesseth, Christian A and Linderman, Scott W and Ranganath, Rajesh and Blei, David M},
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	Year = {2018}}

@inproceedings{maddison2017filtering,
	Author = {Maddison, Chris J and Lawson, John and Tucker, George and Heess, Nicolas and Norouzi, Mohammad and Mnih, Andriy and Doucet, Arnaud and Teh, Yee},
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	Year = {2017}}

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	Author = {Wirnsberger,Peter and Ballard,Andrew J. and Papamakarios,George and Abercrombie,Stuart and Racani\`ere,Sebastien and Pritzel, Alexander and Rezende,Danilo and Blundell,Charles},
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}
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}

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  year={2020},
}

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  volume={9},
  number={2},
  pages={446--482},
  year={2021},
}

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  publisher={Elsevier}
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@inproceedings{corenflos2021differentiable,
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  booktitle={International Conference on Machine Learning},
  year={2021},
}

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@inproceedings{zhangyongxinchen2021path,
  title={Path Integral Sampler: a stochastic control approach for sampling},
  author={Zhang, Qinsheng and Chen, Yongxin},
  booktitle={International Conference on Learning Representations},
  year={2022}
}

@article{vargas2021bayesian,
  title={Bayesian Learning via Neural {S}chr{\"o}dinger--{F}{\"o}llmer Flows},
  author={Vargas, Francisco and Ovsianas, Andrius and Fernandes, David and Girolami, Mark and Lawrence, Neil and N{\"u}sken, Nikolas},
  journal={arXiv preprint arXiv:2111.10510},
  year={2021}
}

@inproceedings{arbel2021annealed,
  title={Annealed flow transport {M}onte {C}arlo},
  author={Arbel, Michael and Matthews, Alex and Doucet, Arnaud},
  booktitle={International Conference on Machine Learning},
  year={2021},
}

@inproceedings{zhangmarzouk2021sampling,
  title={Sampling via Controlled Stochastic Dynamical Systems},
  author={Zhang, Benjamin and Sahai, Tuhin and Marzouk, Youssef},
  booktitle={I (Still) Can't Believe It's Not Better! NeurIPS 2021 Workshop},
  year={2021}
}


@inproceedings{tzen2019theoretical,
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  author={Tzen, Belinda and Raginsky, Maxim},
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  year={2019},
}

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  year={2020}
}

@inproceedings{barrlamacraft2020quantum,
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  author={Barr, Ariel and Gispen, Willem and Lamacraft, Austen},
  booktitle={Mathematical and Scientific Machine Learning},
  year={2020},
}

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  title={Diffusion {S}chr{\"o}dinger Bridge with Applications to Score-Based Generative Modeling},
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  year={2021}
}

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}

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  year={2022}
}


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@book{gine2021mathematical,
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  year={2021},
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}

@article{gottlieb2017efficient,
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  volume={620},
  pages={105--118},
  year={2016},
  publisher={Elsevier}
}


@article{huang2021variational,
  title={A Variational Perspective on Diffusion-Based Generative Models and Score Matching},
  author={Huang, Chin-Wei and Lim, Jae Hyun and Courville, Aaron},
  journal={arXiv preprint arXiv:2106.02808},
  year={2021}
}

@Article{vargasshro2021,
AUTHOR = {Vargas, Francisco and Thodoroff, Pierre and Lamacraft, Austen and Lawrence, Neil},
TITLE = {Solving {S}chr{\"o}dinger Bridges via Maximum Likelihood},
JOURNAL = {Entropy},
VOLUME = {23},
YEAR = {2021},
NUMBER = {9},
ARTICLE-NUMBER = {1134},
URL = {https://www.mdpi.com/1099-4300/23/9/1134},
ISSN = {1099-4300},
ABSTRACT = {The Schrödinger bridge problem (SBP) finds the most likely stochastic evolution between two probability distributions given a prior stochastic evolution. As well as applications in the natural sciences, problems of this kind have important applications in machine learning such as dataset alignment and hypothesis testing. Whilst the theory behind this problem is relatively mature, scalable numerical recipes to estimate the Schrödinger bridge remain an active area of research. Our main contribution is the proof of equivalence between solving the SBP and an autoregressive maximum likelihood estimation objective. This formulation circumvents many of the challenges of density estimation and enables direct application of successful machine learning techniques. We propose a numerical procedure to estimate SBPs using Gaussian process and demonstrate the practical usage of our approach in numerical simulations and experiments.},
DOI = {10.3390/e23091134}
}


@article{heng2020controlled,
  title={Controlled sequential {M}onte {C}arlo},
  author={Heng, Jeremy and Bishop, Adrian N and Deligiannidis, George and Doucet, Arnaud},
  journal={The Annals of Statistics},
  volume={48},
  number={5},
  pages={2904--2929},
  year={2020},
  publisher={Institute of Mathematical Statistics}
}

@article{ruiz2017particle,
  title={Particle smoothing for hidden diffusion processes: Adaptive path integral smoother},
  author={Ruiz, Hans-Christian and Kappen, Hilbert J},
  journal={IEEE Transactions on Signal Processing},
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  number={12},
  pages={3191--3203},
  year={2017},
  publisher={IEEE}
}

@article{thalmeier2020adaptive,
  title={Adaptive Smoothing for Path Integral Control},
  author={Thalmeier, Dominik and Kappen, Hilbert J and Totaro, Simone and G\'omez, Vicenc},
  journal={Journal of Machine Learning Research},
  volume={21},
  pages={1--37},
  year={2020}
}

@inproceedings{lawson2018twisted,
  title={Twisted variational sequential {M}onte {C}arlo},
  author={Lawson, Dieterich and Tucker, George and Naesseth, Christian A and Maddison, Chris and Adams, Ryan P and Teh, Yee Whye},
  booktitle={Third workshop on Bayesian Deep Learning (NeurIPS)},
  year={2018}
}

@article{nusken2021solving,
  title={Solving high-dimensional {H}amilton--{J}acobi--{B}ellman {PDE}s using neural networks: perspectives from the theory of controlled diffusions and measures on path space},
  author={N{\"u}sken, Nikolas and Richter, Lorenz},
  journal={Partial Differential Equations and Applications},
  volume={2},
  number={4},
  pages={1--48},
  year={2021},
  publisher={Springer}
}

@article{hartmann2019variational,
  title={Variational approach to rare event simulation using least-squares regression},
  author={Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz},
  journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume={29},
  number={6},
  pages={063107},
  year={2019},
  publisher={AIP Publishing LLC}
}

@article{zhang2021path,
  title={Path Integral Sampler: a stochastic control approach for sampling},
  author={Zhang, Qinsheng and Chen, Yongxin},
  journal={arXiv preprint arXiv:2111.15141},
  year={2021}
}

@article{ruzayqat2022unbiased,
  title={Unbiased Estimation using a Class of Diffusion Processes},
  author={Ruzayqat, Hamza and Beskos, Alexandros and Crisan, Dan and Jasra, Ajay and Kantas, Nikolas},
  journal={arXiv preprint arXiv:2203.03013},
  year={2022}
}


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  title={On the relative entropy of discrete-time {M}arkov processes with given end-point densities},
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  journal={arXiv preprint arXiv:2104.07708},
  year={2021}
}


@article{tamar2016value,
  title={Value iteration networks},
  author={Tamar, Aviv and Wu, Yi and Thomas, Garrett and Levine, Sergey and Abbeel, Pieter},
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  volume={29},
  year={2016}
}
@article{fulop2021efficient,
  title={Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models},
  author={Fulop, Andras and Heng, Jeremy and Li, Junye},
  journal={Available at SSRN 3878869},
  year={2021}
}



@article{saremi2019neural,
  title={Neural empirical bayes},
  author={Saremi, Saeed and Hyvarinen, Aapo},
  journal={arXiv preprint arXiv:1903.02334},
  year={2019}
}

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  title={Robust {B}ayesian estimation for the linear model and robustifying the {K}alman filter},
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  number={3},
  pages={361--371},
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  publisher={IEEE}
}

@article{vono2022efficient,
  title={Efficient {MCMC} sampling with dimension-free convergence rate using {ADMM}-type splitting},
  author={Vono, Maxime and Paulin, Daniel and Doucet, Arnaud},
  journal={Journal of Machine Learning Research},
  volume={23},
  number={25},
  year={2022},
}

@article{liang2022proximal,
  title={A Proximal Algorithm for Sampling},
  author={Liang, Jiaming and Chen, Yongxin},
  journal={arXiv preprint arXiv:2202.13975},
  year={2022}
}

%% This BibTeX bibliography file was created using BibDesk.
%% http://bibdesk.sourceforge.net/

%% Created for Michael N. Arbel at 2021-02-08 16:08:23 +0000 


%% Saved with string encoding Unicode (UTF-8) 
@misc{Rippel2013,
      title={High-Dimensional Probability Estimation with Deep Density Models}, 
      author={Oren Rippel and Ryan Prescott Adams},
      year={2013},
      eprint={1302.5125},
      archivePrefix={arXiv},
      primaryClass={stat.ML}
}

@inproceedings{Dinh2015,
  author    = {Laurent Dinh and
               David Krueger and
               Yoshua Bengio},
  title     = {{NICE:} Non-linear Independent Components Estimation},
  booktitle = {3rd International Conference on Learning Representations, {ICLR}},
  year      = {2015}
}


@inproceedings{Zimmermann:2021,
	Author = {Heiko Zimmermann and Hao Wu and Babak Esmaeili and Jan-Willem van de Meent},
	Booktitle = {Advances in Neural Information Processing Systems},
    Title = {Nested Variational Inference},
	Year = {2021}
}


@inproceedings{Kingma:2016,
	Author = {Kingma, Durk P and Salimans, Tim and Jozefowicz, Rafal and Chen, Xi and Sutskever, Ilya and Welling, Max},
	Booktitle = {Advances in Neural Information Processing Systems},
	Title = {Improved Variational Inference with Inverse Autoregressive Flow},
	Year = {2016}}

@article{Neal:2012,
	Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	Adsurl = {https://ui.adsabs.harvard.edu/abs/2012arXiv1206.1901N},
	Archiveprefix = {arXiv},
	Author = {{Neal}, Radford M.},
	Eid = {arXiv:1206.1901},
	Eprint = {1206.1901},
	Journal = {arXiv e-prints},
	Keywords = {Statistics - Computation, Physics - Computational Physics},
	Month = jun,
	Pages = {arXiv:1206.1901},
	Primaryclass = {stat.CO},
	Title = {{MCMC using Hamiltonian dynamics}},
	Year = 2012}

@article{Beskos:2011,
	Author = {A. Beskos and F.J. Pinski and J.M. Sanz-Serna and A.M. Stuart},
	Issn = {0304-4149},
	Journal = {Stochastic Processes and their Applications},
	Number = {10},
	Pages = {2201 - 2230},
	Title = {Hybrid {M}onte {C}arlo on {H}ilbert spaces},
	Volume = {121},
	Year = {2011},}

@article{lee2010utility,
	Author = {Lee, Anthony and Yau, Christopher and Giles, Michael B and Doucet, Arnaud and Holmes, Chris C},
	Journal = {Journal of Computational and Graphical Statistics},
	Number = {4},
	Pages = {769--789},
	Publisher = {ASA},
	Title = {On the utility of graphics cards to perform massively parallel simulation of advanced Monte Carlo methods},
	Volume = {19},
	Year = {2010}}

@inproceedings{Durkan:2019,
	Author = {Durkan, Conor and Bekasov, Artur and Murray, Iain and Papamakarios, George},
	Booktitle = {Advances in Neural Information Processing Systems},
	Title = {Neural Spline Flows},
	Year = {2019},}


@article{Dillon:2017,
	Adsnote = {Provided by the SAO/NASA Astrophysics Data System},
	Author = {{Dillon}, Joshua V. and {Langmore}, Ian and {Tran}, Dustin and {Brevdo}, Eugene and {Vasudevan}, Srinivas and {Moore}, Dave and {Patton}, Brian and {Alemi}, Alex and {Hoffman}, Matt and {Saurous}, Rif A.},
	Journal = {arXiv preprint arXiv:1711.10604},
	Title = {{TensorFlow Distributions}},
	Year = 2017}

@software{Hennigan:2020,
	Author = {Tom Hennigan and Trevor Cai and Tamara Norman and Igor Babuschkin},
	Title = {{H}aiku: {S}onnet for {JAX}},
	Version = {0.0.3},
	Year = {2020},}

@software{Bradbury:2018,
	Author = {James Bradbury and Roy Frostig and Peter Hawkins and Matthew James Johnson and Chris Leary and Dougal Maclaurin and George Necula and Adam Paszke and Jake Vander{P}las and Skye Wanderman-{M}ilne and Qiao Zhang},
	Title = {{JAX}: composable transformations of {P}ython+{N}um{P}y programs},
	Version = {0.2.5},
	Year = {2018},}


@article{Hoffman:2014,
	Author = {Matthew D. Hoffman and Andrew Gelman},
	Journal = {Journal of Machine Learning Research},
	Number = {47},
	Pages = {1593-1623},
	Title = {The {N}o-{U}-{T}urn {S}ampler: Adaptively Setting Path Lengths in {H}amiltonian Monte Carlo},
	Url = {http://jmlr.org/papers/v15/hoffman14a.html},
	Volume = {15},
	Year = {2014}}


@article{Behr:2018,
	Annote = {Comment: 30 pages, 51 figures},
	Author = {Behr, Maximilian and Benner, Peter and Heiland, Jan},
	Journal = {arXiv:1811.08327 [math]},
	Keywords = {15A24, 65F60, 65L05, Mathematics - Numerical Analysis},
	Month = nov,
	Note = {arXiv: 1811.08327},
	Title = {Solution {Formulas} for {Differential} {Sylvester} and {Lyapunov} {Equations}},
	Url = {http://arxiv.org/abs/1811.08327},
	Urldate = {2019-10-24},
	Year = {2018}}

@article{Carrillo:2006,
	Abstract = {An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) --- if uniformly controlled --- will quantify contractivity (limit expansivity) of the flow.},
	Author = {Carrillo, Jos{\'e} A. and McCann, Robert J. and Villani, C{\'e}dric},
	Date-Added = {2019-07-27 15:18:39 +0000},
	Date-Modified = {2019-07-27 15:18:39 +0000},
	Doi = {10.1007/s00205-005-0386-1},
	Issn = {1432-0673},
	Journal = {Archive for Rational Mechanics and Analysis},
	Keywords = {Complex System, Decay Rate, Manifold, Neural Network, Nonlinear Dynamics},
	Language = {en},
	Month = feb,
	Number = {2},
	Pages = {217--263},
	Title = {Contractions in the 2-{Wasserstein} {Length} {Space} and {Thermalization} of {Granular} {Media}},
	Url = {https://doi.org/10.1007/s00205-005-0386-1},
	Urldate = {2019-07-27},
	Volume = {179},
	Year = {2006},
	Bdsk-Url-1 = {https://doi.org/10.1007/s00205-005-0386-1}}

@article{kondratyev2016new,
	Author = {Kondratyev, Stanislav and Monsaingeon, L{\'e}onard and Vorotnikov, Dmitry and others},
	Journal = {Advances in Differential Equations},
	Title = {A new optimal transport distance on the space of finite Radon measures},
	Year = {2016}}

@article{liero2016optimal,
	Author = {Liero, Matthias and Mielke, Alexander and Savar{\'e}, Giuseppe},
	Journal = {SIAM Journal on Mathematical Analysis},
	Title = {Optimal Transport in Competition with Reaction: The Hellinger--Kantorovich Distance and Geodesic Curves},
	Year = {2016}}

@article{Chizat:2015,
	Author = {Chizat, Lenaic and Schmitzer, Bernhard and Peyr{\'e}, Gabriel and Vialard, Fran{\c c}ois-Xavier},
	Journal = {arXiv:1506.06430 [math]},
	Title = {An {Interpolating} {Distance} between {Optimal} {Transport} and {Fisher}-{Rao}},
	Url = {http://arxiv.org/abs/1506.06430},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1506.06430}}

@article{Shestakov:2009,
	Author = {Shestakov, Ivan V. and Shlapunov, Alexander A.},
	Date-Added = {2019-06-10 23:02:02 +0000},
	Date-Modified = {2019-06-10 23:02:02 +0000},
	Language = {en},
	Month = jan,
	Title = {Negative {Sobolev} {Spaces} in the {Cauchy} {Problem} for the {Cauchy}-{Riemann} {Operator}},
	Url = {http://elib.sfu-kras.ru/handle/2311/877},
	Urldate = {2019-06-10},
	Year = {2009},
	Bdsk-Url-1 = {http://elib.sfu-kras.ru/handle/2311/877}}

@article{Chizat:2018a,
	Author = {Chizat, Lenaic and Bach, Francis},
	Journal = {arXiv:1812.07956 [cs, math]},
	Month = dec,
	Note = {arXiv: 1812.07956},
	Title = {A {Note} on {Lazy} {Training} in {Supervised} {Differentiable} {Programming}},
	Url = {http://arxiv.org/abs/1812.07956},
	Urldate = {2019-05-05},
	Year = {2018},
	Bdsk-Url-1 = {http://arxiv.org/abs/1812.07956}}

@book{Villani:2003,
	Author = {Villani, Cedric},
	Date-Added = {2019-05-23 19:24:39 +0000},
	Date-Modified = {2019-05-23 19:24:40 +0000},
	Isbn = {978-0-8218-3312-4},
	Keywords = {Mathematics / General},
	Language = {en},
	Publisher = {American Mathematical Soc.},
	Title = {Topics in {Optimal} {Transportation}},
	Year = {2003}}

@article{dalalyan2019user,
	Author = {Dalalyan, Arnak S and Karagulyan, Avetik},
	Journal = {Stochastic Processes and their Applications},
	Publisher = {Elsevier},
	Title = {User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient},
	Year = {2019}}

@article{benamou2000computational,
	Author = {Benamou, Jean-David and Brenier, Yann},
	Journal = {Numerische Mathematik},
	Number = {3},
	Pages = {375--393},
	Publisher = {Springer},
	Title = {A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem},
	Volume = {84},
	Year = {2000}}

@article{oguntuase2001inequality,
	Author = {Oguntuase, James Adedayo},
	Journal = {Journal of Inequalities in Pure and Applied Mathematics},
	Title = {On an inequality of Gronwall},
	Year = {2001}}

@article{carrillo2006contractions,
	Author = {Carrillo, Jos{\'e} A and McCann, Robert J and Villani, C{\'e}dric},
	Journal = {Archive for Rational Mechanics and Analysis},
	Number = {2},
	Pages = {217--263},
	Publisher = {Springer},
	Title = {Contractions in the 2-Wasserstein length space and thermalization of granular media},
	Volume = {179},
	Year = {2006}}

@article{Sirignano:2018,
	Abstract = {Machine learning, and in particular neural network models, have revolutionized fields such as image, text, and speech recognition. Today, many important real-world applications in these areas are driven by neural networks. There are also growing applications in engineering, robotics, medicine, and finance. Despite their immense success in practice, there is limited mathematical understanding of neural networks. This paper illustrates how neural networks can be studied via stochastic analysis, and develops approaches for addressing some of the technical challenges which arise. We analyze one-layer neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously prove that the empirical distribution of the neural network parameters converges to the solution of a nonlinear partial differential equation. This result can be considered a law of large numbers for neural networks. In addition, a consequence of our analysis is that the trained parameters of the neural network asymptotically become independent, a property which is commonly called "propagation of chaos".},
	Author = {Sirignano, Justin and Spiliopoulos, Konstantinos},
	Date-Added = {2019-05-21 23:57:16 +0000},
	Date-Modified = {2019-05-21 23:57:16 +0000},
	Journal = {arXiv:1805.01053 [math]},
	Keywords = {Mathematics - Probability},
	Month = may,
	Note = {arXiv: 1805.01053},
	Title = {Mean {Field} {Analysis} of {Neural} {Networks}},
	Url = {http://arxiv.org/abs/1805.01053},
	Urldate = {2019-05-21},
	Year = {2018},
	Bdsk-Url-1 = {http://arxiv.org/abs/1805.01053}}

@article{Dziugaite:2015a,
	Abstract = {We consider training a deep neural network to generate samples from an unknown distribution given i.i.d. data. We frame learning as an optimization minimizing a two-sample test statistic---informally speaking, a good generator network produces samples that cause a two-sample test to fail to reject the null hypothesis. As our two-sample test statistic, we use an unbiased estimate of the maximum mean discrepancy, which is the centerpiece of the nonparametric kernel two-sample test proposed by Gretton et al. (2012). We compare to the adversarial nets framework introduced by Goodfellow et al. (2014), in which learning is a two-player game between a generator network and an adversarial discriminator network, both trained to outwit the other. From this perspective, the MMD statistic plays the role of the discriminator. In addition to empirical comparisons, we prove bounds on the generalization error incurred by optimizing the empirical MMD.},
	Annote = {Comment: 10 pages, to appear in Uncertainty in Artificial Intelligence (UAI) 2015},
	Author = {Dziugaite, Gintare Karolina and Roy, Daniel M. and Ghahramani, Zoubin},
	Date-Added = {2019-05-21 23:56:45 +0000},
	Date-Modified = {2019-05-21 23:56:45 +0000},
	Journal = {arXiv:1505.03906 [cs, stat]},
	Keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
	Month = may,
	Note = {arXiv: 1505.03906},
	Title = {Training generative neural networks via {Maximum} {Mean} {Discrepancy} optimization},
	Url = {http://arxiv.org/abs/1505.03906},
	Urldate = {2019-05-21},
	Year = {2015},
	Bdsk-Url-1 = {http://arxiv.org/abs/1505.03906}}

@article{Uppal:2019,
	Author = {Uppal, Ananya and Singh, Shashank and P{\'o}czos, Barna{\'a}s},
	Journal = {arXiv preprint arXiv:1902.03511},
	Title = {Nonparametric Density Estimation under Besov IPM Losses},
	Year = {2019}}

@article{Li:2015,
	Author = {Li, Yujia and Swersky, Kevin and Zemel, Richard},
	Journal = {arXiv preprint arXiv:1502.02761},
	Title = {Generative moment matching networks},
	Year = {2015}}

@article{Li:2017a,
	Abstract = {Generative moment matching network (GMMN) is a deep generative model that differs from Generative Adversarial Network (GAN) by replacing the discriminator in GAN with a two-sample test based on kernel maximum mean discrepancy (MMD). Although some theoretical guarantees of MMD have been studied, the empirical performance of GMMN is still not as competitive as that of GAN on challenging and large benchmark datasets. The computational efficiency of GMMN is also less desirable in comparison with GAN, partially due to its requirement for a rather large batch size during the training. In this paper, we propose to improve both the model expressiveness of GMMN and its computational efficiency by introducing adversarial kernel learning techniques, as the replacement of a fixed Gaussian kernel in the original GMMN. The new approach combines the key ideas in both GMMN and GAN, hence we name it MMD GAN. The new distance measure in MMD GAN is a meaningful loss that enjoys the advantage of weak topology and can be optimized via gradient descent with relatively small batch sizes. In our evaluation on multiple benchmark datasets, including MNIST, CIFAR- 10, CelebA and LSUN, the performance of MMD-GAN significantly outperforms GMMN, and is competitive with other representative GAN works.},
	Annote = {Comment: In the Proceedings of Thirty-first Annual Conference on Neural Information Processing Systems (NIPS 2017)},
	Author = {Li, Chun-Liang and Chang, Wei-Cheng and Cheng, Yu and Yang, Yiming and P{\'o}czos, Barnab{\'a}s},
	Date-Added = {2019-05-21 16:17:09 +0000},
	Date-Modified = {2019-05-21 16:17:09 +0000},
	Journal = {arXiv:1705.08584 [cs, stat]},
	Keywords = {Statistics - Machine Learning, Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
	Month = may,
	Note = {arXiv: 1705.08584},
	Shorttitle = {{MMD} {GAN}},
	Title = {{MMD} {GAN}: {Towards} {Deeper} {Understanding} of {Moment} {Matching} {Network}},
	Url = {http://arxiv.org/abs/1705.08584},
	Urldate = {2018-11-13},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1705.08584}}

@article{Bolte:2016,
	Author = {Blanchet, Adrien and Bolte, J{\'e}r{\^o}me},
	Journal = {Journal of Functional Analysis},
	Number = {7},
	Pages = {1650--1673},
	Publisher = {Elsevier},
	Title = {A family of functional inequalities: {\L}ojasiewicz inequalities and displacement convex functions},
	Volume = {275},
	Year = {2018}}

@book{Steinwart:2008a,
	Author = {Steinwart, Ingo and Christmann, Andreas},
	Date-Added = {2019-05-19 11:35:35 +0000},
	Date-Modified = {2019-05-19 11:35:35 +0000},
	Edition = {1st},
	Isbn = {0387772413},
	Publisher = {Springer Publishing Company, Incorporated},
	Title = {Support Vector Machines},
	Year = {2008}}

@inproceedings{Mroueh:2019,
	Author = {Mroueh, Youssef and Sercu, Tom and Raj, Anant},
	Booktitle = {AISTATS},
	Title = {Sobolev Descent},
	Year = {2019}}

@article{Peyre:2011,
	Author = {Peyre, R{\'e}mi},
	Journal = {ESAIM: Control, Optimisation and Calculus of Variations},
	Number = {4},
	Pages = {1489--1501},
	Publisher = {EDP Sciences},
	Title = {Comparison between {$W_2$} distance and {$\dot{H}^{-1}$} norm, and localisation of {Wasserstein} distance},
	Volume = {24},
	Year = {2018}}

@article{Otto:2000,
	Author = {Otto, Felix and Villani, C{\'e}dric},
	Journal = {Journal of Functional Analysis},
	Number = {2},
	Pages = {361--400},
	Publisher = {Elsevier},
	Title = {Generalization of an inequality by Talagrand and links with the logarithmic Sobolev inequality},
	Volume = {173},
	Year = {2000}}

@article{carrillo2019blob,
	Author = {Carrillo, Jos{\'e} Antonio and Craig, Katy and Patacchini, Francesco S},
	Date-Added = {2019-05-17 17:13:25 +0000},
	Date-Modified = {2019-05-17 17:13:25 +0000},
	Journal = {Calculus of Variations and Partial Differential Equations},
	Number = {2},
	Pages = {53},
	Publisher = {Springer},
	Title = {A blob method for diffusion},
	Volume = {58},
	Year = {2019}}

@article{craig2016blob,
	Author = {Craig, Katy and Bertozzi, Andrea},
	Date-Added = {2019-05-17 17:13:11 +0000},
	Date-Modified = {2019-05-17 17:13:11 +0000},
	Journal = {Mathematics of computation},
	Number = {300},
	Pages = {1681--1717},
	Title = {A blob method for the aggregation equation},
	Volume = {85},
	Year = {2016}}

@article{Chaudhari:2017,
	Author = {Chaudhari, Pratik and Oberman, Adam and Osher, Stanley and Soatto, Stefano and Carlier, Guillaume},
	Journal = {arXiv:1704.04932 [cs, math]},
	Title = {Deep {Relaxation}: partial differential equations for optimizing deep neural networks},
	Url = {http://arxiv.org/abs/1704.04932},
	Year = {2017},
	Bdsk-Url-1 = {http://arxiv.org/abs/1704.04932}}

@inproceedings{Hazan:2015,
	Author = {Hazan, Elad and Levy, Kfir Yehuda and Shalev-Shwartz, Shai},
	Booktitle = {ICML},
	Title = {On graduated optimization for stochastic non-convex problems},
	Year = {2016}}

@article{Gulcehre:2016,
	Author = {Gulcehre, Caglar and Moczulski, Marcin and Visin, Francesco and Bengio, Yoshua},
	Journal = {arXiv preprint arXiv:1608.04980},
	Title = {Mollifying networks},
	Year = {2016}}

@article{Mobahi:2016,
	Abstract = {This work presents a new algorithm for training recurrent neural networks (although ideas are applicable to feedforward networks as well). The algorithm is derived from a theory in nonconvex optimization related to the diffusion equation. The contributions made in this work are two fold. First, we show how some seemingly disconnected mechanisms used in deep learning such as smart initialization, annealed learning rate, layerwise pretraining, and noise injection (as done in dropout and SGD) arise naturally and automatically from this framework, without manually crafting them into the algorithms. Second, we present some preliminary results on comparing the proposed method against SGD. It turns out that the new algorithm can achieve similar level of generalization accuracy of SGD in much fewer number of epochs.},
	Author = {Mobahi, Hossein},
	Date-Added = {2019-05-17 16:53:44 +0000},
	Date-Modified = {2019-05-17 16:53:44 +0000},
	Journal = {arXiv:1601.04114 [cs]},
	Keywords = {Computer Science - Machine Learning},
	Month = jan,
	Note = {arXiv: 1601.04114},
	Title = {Training {Recurrent} {Neural} {Networks} by {Diffusion}},
	Url = {http://arxiv.org/abs/1601.04114},
	Urldate = {2019-05-17},
	Year = {2016},
	Bdsk-Url-1 = {http://arxiv.org/abs/1601.04114}}

@inproceedings{Gulcehre:2016a,
	Author = {Gulcehre, Caglar and Moczulski, Marcin and Denil, Misha and Bengio, Yoshua},
	Booktitle = {ICML},
	Title = {Noisy activation functions},
	Year = {2016}}

@article{tolstikhin2017minimax,
	Author = {Tolstikhin, Ilya and Sriperumbudur, Bharath K and Muandet, Krikamol},
	Journal = {The Journal of Machine Learning Research},
	Number = {1},
	Pages = {3002--3048},
	Publisher = {JMLR. org},
	Title = {Minimax estimation of kernel mean embeddings},
	Volume = {18},
	Year = {2017}}

@article{herrmann2010non,
	Author = {Herrmann, Samuel and Tugaut, Julian},
	Journal = {Stochastic Processes and their Applications},
	Number = {7},
	Pages = {1215--1246},
	Publisher = {Elsevier},
	Title = {Non-uniqueness of stationary measures for self-stabilizing processes},
	Volume = {120},
	Year = {2010}}

@article{tugaut2014phase,
	Author = {Tugaut, Julian},
	Journal = {Stochastics An International Journal of Probability and Stochastic Processes},
	Number = {2},
	Pages = {257--284},
	Publisher = {Taylor \& Francis},
	Title = {Phase transitions of McKean--Vlasov processes in double-wells landscape},
	Volume = {86},
	Year = {2014}}

@article{tugaut2013convergence,
	Author = {Tugaut, Julian and others},
	Journal = {The Annals of Probability},
	Number = {3A},
	Pages = {1427--1460},
	Publisher = {Institute of Mathematical Statistics},
	Title = {Convergence to the equilibria for self-stabilizing processes in double-well landscape},
	Volume = {41},
	Year = {2013}}

@article{tugaut2014self,
	Author = {Tugaut, Julian},
	Journal = {Journal of Theoretical Probability},
	Number = {1},
	Pages = {57--79},
	Publisher = {Springer},
	Title = {Self-stabilizing Processes in Multi-wells Landscape in $\mathbb{R}^d$-Invariant Probabilities},
	Volume = {27},
	Year = {2014}}

@article{sutherland2017efficient,
	Author = {Sutherland, Dougal J and Strathmann, Heiko and Arbel, Michael and Gretton, Arthur},
	Journal = {AISTATS},
	Title = {Efficient and principled score estimation with Nystr{\"o}m kernel exponential families},
	Year = {2018}}

@inproceedings{csimcsekli2018sliced,
	Author = {{\c{S}}im{\c{s}}ekli, Umut and Liutkus, Antoine and Majewski, Szymon and Durmus, Alain},
	Booktitle = {ICML},
	Title = {Sliced-Wasserstein flows: Nonparametric generative modeling via optimal transport and diffusions},
	Year = {2019}}

@article{rotskoff2018neural,
	Author = {Rotskoff, Grant M and Vanden-Eijnden, Eric},
	Journal = {arXiv preprint arXiv:1805.00915},
	Title = {Neural networks as interacting particle systems: Asymptotic convexity of the loss landscape and universal scaling of the approximation error},
	Year = {2018}}

@article{mei2018mean,
	Author = {Mei, Song and Montanari, Andrea and Nguyen, Phan-Minh},
	Journal = {Proceedings of the National Academy of Sciences},
	Number = {33},
	Pages = {E7665--E7671},
	Publisher = {National Acad Sciences},
	Title = {A mean field view of the landscape of two-layer neural networks},
	Volume = {115},
	Year = {2018}}

@article{sirignano2018mean,
	Author = {Sirignano, Justin and Spiliopoulos, Konstantinos},
	Journal = {arXiv preprint arXiv:1808.09372},
	Title = {Mean field analysis of neural networks: A central limit theorem},
	Year = {2018}}

@book{smola1998learning,
	Author = {Smola, Alex J and Scholkopf, Bernhard},
	Publisher = {Citeseer},
	Title = {Learning with kernels},
	Volume = {4},
	Year = {1998}}

@misc{pavliotis2011stochastic,
	Author = {Pavliotis, Grigorios A},
	Publisher = {Springer},
	Title = {Stochastic processes and applications},
	Year = {2011}}

@article{mckean1966class,
	Author = {McKean Jr, HP},
	Journal = {Proceedings of the National Academy of Sciences of the United States of America},
	Number = {6},
	Pages = {1907},
	Publisher = {National Academy of Sciences},
	Title = {A class of Markov processes associated with nonlinear parabolic equations},
	Volume = {56},
	Year = {1966}}

@article{durmus2018elementary,
	Author = {Durmus, Alain and Eberle, Andreas and Guillin, Arnaud and Zimmer, Raphael},
	Journal = {arXiv preprint arXiv:1805.11387},
	Title = {An elementary approach to uniform in time propagation of chaos},
	Year = {2018}}

@inproceedings{kac1956foundations,
	Author = {Kac, Mark},
	Booktitle = {Proceedings of The third Berkeley symposium on mathematical statistics and probability},
	Organization = {University of California Press Berkeley and Los Angeles, California},
	Pages = {171--197},
	Title = {Foundations of kinetic theory},
	Volume = {3},
	Year = {1956}}

@inproceedings{chizat2018global,
	Author = {Chizat, Lenaic and Bach, Francis},
	Publisher = {NIPS},
	Title = {On the global convergence of gradient descent for over-parameterized models using optimal transport},
	Year = {2018}}

@article{dudley1969speed,
	Author = {Dudley, RM},
	Journal = {The Annals of Mathematical Statistics},
	Number = {1},
	Pages = {40--50},
	Publisher = {JSTOR},
	Title = {The speed of mean Glivenko-Cantelli convergence},
	Volume = {40},
	Year = {1969}}

@article{weed2017sharp,
	Author = {Weed, Jonathan and Bach, Francis},
	Journal = {arXiv preprint arXiv:1707.00087},
	Title = {Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance},
	Year = {2017}}

@article{jourdain2007nonlinear,
	Author = {Jourdain, Benjamin and M{\'e}l{\'e}ard, Sylvie and Woyczynski, Wojbor},
	Journal = {arXiv preprint arXiv:0707.2723},
	Title = {Nonlinear SDEs driven by Levy proesses and related PDEs},
	Year = {2007}}

@article{sriperumbudur2010hilbert,
	Author = {Sriperumbudur, Bharath K and Gretton, Arthur and Fukumizu, Kenji and Sch{\"o}lkopf, Bernhard and Lanckriet, Gert RG},
	Journal = {Journal of Machine Learning Research},
	Number = {Apr},
	Pages = {1517--1561},
	Title = {Hilbert space embeddings and metrics on probability measures},
	Volume = {11},
	Year = {2010}}

@incollection{sznitman1991topics,
	Author = {Sznitman, Alain-Sol},
	Booktitle = {Ecole d'{\'e}t{\'e} de probabilit{\'e}s de Saint-Flour},
	Pages = {165--251},
	Publisher = {Springer},
	Title = {Topics in propagation of chaos},
	Year = {1991}}

@inproceedings{rotskoff2019global,
	Author = {Rotskoff, Grant and Jelassi, Samy and Bruna, Joan and Vanden-Eijnden, Eric},
	Booktitle = {ICML},
	Title = {Global convergence of neuron birth-death dynamics},
	Year = {2019}}

@article{mroueh2018regularized,
	Author = {Mroueh, Youssef and Sercu, Tom and Raj, Anant},
	Journal = {arXiv preprint arXiv:1805.12062},
	Title = {Regularized Kernel and Neural Sobolev Descent: Dynamic MMD Transport},
	Year = {2018}}

@article{shi2018spectral,
	Author = {Shi, Jiaxin and Sun, Shengyang and Zhu, Jun},
	Journal = {ICML},
	Title = {A spectral approach to gradient estimation for implicit distributions},
	Year = {2018}}

@article{li2018gradient,
	Author = {Li, Yingzhen and Turner, Richard E},
	Journal = {ICLR},
	Title = {Gradient estimators for implicit models},
	Year = {2018}}

@book{ito1951stochastic,
	Author = {It{\^o}, Kiyosi},
	Publisher = {American Mathematical Soc.},
	Title = {On stochastic differential equations},
	Volume = {4},
	Year = {1951}}

@article{Arbel:2018,
	Author = {Arbel, Michael and Sutherland, Dougal J. and Bi{\'n}kowski, Miko{\l}aj and Gretton, Arthur},
	Journal = {NIPS},
	Title = {On gradient regularizers for {MMD} {GANs}},
	Year = {2018}}

@article{Santambrogio:2015,
	Author = {Santambrogio, Filippo},
	Journal = {Birk{\"a}user, NY},
	Pages = {58--63},
	Publisher = {Springer},
	Title = {Optimal transport for applied mathematicians},
	Volume = {55},
	Year = {2015}}

@article{santambrogio2017euclidean,
	Author = {Santambrogio, Filippo},
	Journal = {Bulletin of Mathematical Sciences},
	Number = {1},
	Pages = {87--154},
	Publisher = {Springer},
	Title = {$\{$Euclidean, metric, and Wasserstein$\}$ gradient flows: an overview},
	Volume = {7},
	Year = {2017}}

@book{ambrosio2008gradient,
	Author = {Ambrosio, Luigi and Gigli, Nicola and Savar{\'e}, Giuseppe},
	Publisher = {Springer Science \& Business Media},
	Title = {Gradient flows: in metric spaces and in the space of probability measures},
	Year = {2008}}

@article{wibisono2018sampling,
	Author = {Wibisono, Andre},
	Journal = {arXiv preprint arXiv:1802.08089},
	Title = {Sampling as optimization in the space of measures: The Langevin dynamics as a composite optimization problem},
	Year = {2018}}

@article{mmd-jmlr,
	Author = {Gretton, A. and Borgwardt, K. M. and Rasch, M. J. and Sch{\"{o}}lkopf, B. and Smola, A. J.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {JMLR},
	Title = {A Kernel Two-Sample Test},
	Volume = {13},
	Year = {2012}}

@inproceedings{likelihoods-vs-samples,
	Archiveprefix = {arXiv},
	Author = {Theis, L. and van den Oord, A. and Bethge, M.},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1511.01844},
	Title = {A note on the evaluation of generative models},
	Year = {2016}}

@misc{note-on-inception,
	Archiveprefix = {arXiv},
	Author = {Shane Barratt and Rishi Sharma},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1801.01973},
	Title = {A Note on the Inception Score},
	Year = {2018}}

@article{owen:integrals,
	Author = {Owen, D. B.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Number = {4},
	Pages = {389--419},
	Title = {A table of normal integrals},
	Volume = {9},
	Year = {1980}}

@inproceedings{3sample,
	Archiveprefix = {arXiv},
	Author = {W. Bounliphone and E. Belilovsky and M. B. Blaschko and I. Antonoglou and A. Gretton},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1511.04581},
	Title = {A Test of Relative Similarity For Model Selection in Generative Models},
	Year = {2016}}

@inproceedings{adam,
	Archiveprefix = {arXiv},
	Author = {Kingma, D. and Ba, J.},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1412.6980},
	Title = {Adam: A Method for Stochastic Optimization},
	Year = {2015}}

@misc{empirical-evaluation,
	Author = {Gao Huang and Yang Yuan and Qiantong Xu and Chuan Guo and Yu Sun and Felix Wu and Kilian Weinberger},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {An empirical study on evaluation metrics of generative adversarial networks},
	Url = {https://openreview.net/forum?id=Sy1f0e-R-},
	Year = {2018},
	Bdsk-Url-1 = {https://openreview.net/forum?id=Sy1f0e-R-}}

@inproceedings{approx-convergence-props,
	Archiveprefix = {arXiv},
	Author = {Liu, S. and Bousquet, O. and Chaudhuri, K.},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1705.08991},
	Title = {Approximation and Convergence Properties of Generative Adversarial Learning},
	Year = {2017}}

@misc{began,
	Archiveprefix = {arXiv},
	Author = {D. Berthelot and T. Schumm and L. Metz},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1703.10717},
	Title = {{BEGAN}: Boundary Equilibrium Generative Adversarial Networks},
	Year = {2017}}

@inproceedings{BenMesDauRif13,
	Archiveprefix = {arXiv},
	Author = {Y. Bengio and G. Mesnil and Y. Dauphin and S. Rifai},
	Booktitle = {ICML},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1207.4404},
	Title = {Better mixing via deep representations},
	Year = {2013}}

@inproceedings{beyond-face-rotation,
	Archiveprefix = {arXiv},
	Author = {R. Huang and S. Zhang and T. Li and R. He},
	Booktitle = {ICCV},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1704.04086},
	Title = {Beyond Face Rotation: Global and Local Perception {GAN} for Photorealistic and Identity Preserving Frontal View Synthesis},
	Year = {2017}}

@inproceedings{Hjelm:2018,
	Author = {Hjelm, {R. Devon} and Jacob, {Athul Paul} and Che, Tong and Trischler, Adam and Cho, Kyunghyun and Bengio,Yoshua},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Boundary-Seeking Generative Adversarial Networks},
	Year = {2018}}

@inproceedings{b-test,
	Archiveprefix = {arXiv},
	Author = {Zaremba, W. and Gretton, A. and Blaschko, M. B.},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1307.1954},
	Title = {B-tests: Low Variance Kernel Two-Sample Tests},
	Year = {2013}}

@misc{gan-vs-ml-realnvp,
	Archiveprefix = {arXiv},
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	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
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@inproceedings{coulomb-gan,
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
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	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1707.00087},
	Title = {Sharp asymptotic and finite-sample rates of convergence of empirical measures in Wasserstein distance},
	Year = {2017}}

@misc{sobolev-descent,
	Author = {Mroueh, Youssef and Sercu, Tom and Raj, Anant},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Month = 4,
	Note = {Private communication},
	Title = {Sobolev Descent: Variational Transport of Distributions via Advection},
	Year = {2018}}

@inproceedings{sobolev-gan,
	Author = {Mroueh, Youssef and Li, Chung-Liang and Sercu, Tom and Raj, Anant and Cheng, Yu},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Title = {Sobolev GAN},
	Year = {2018}}

@inproceedings{Miyato:2018,
	Archiveprefix = {arXiv},
	Author = {Miyato, Takeru and Kataoka, Toshiki and Koyama, Masanori and Yoshida, Yuichi},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1802.05927},
	Title = {Spectral Normalization for Generative Adversarial Networks},
	Year = {2018}}

@inproceedings{roth:regularization,
	Archiveprefix = {arXiv},
	Author = {Roth, Kevin and Lucchi, Aurelien and Nowozin, Sebastian and Hofmann, Thomas},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1705.09367},
	Title = {Stabilizing Training of Generative Adversarial Networks through Regularization},
	Year = {2017}}

@inproceedings{stacked-gans,
	Archiveprefix = {arXiv},
	Author = {Huang, X. and Li, Y. and Poursaeed, O. and Hopcroft, J. and Belongie, S.},
	Booktitle = {CVPR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1612.04357},
	Title = {Stacked Generative Adversarial Networks},
	Year = {2017}}

@article{GneRaf07,
	Author = {T. Gneiting and A. E. Raftery},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {JASA},
	Number = {477},
	Pages = {359--378},
	Title = {Strictly proper scoring rules, prediction, and estimation},
	Volume = {102},
	Year = {2007}}

@book{SteChr08,
	Author = {I. Steinwart and A. Christmann},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Publisher = {Springer},
	Series = {Information Science and Statistics},
	Title = {Support Vector Machines},
	Year = {2008}}

@article{Zahorski:1946,
	Author = {Zahorski, Z.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Bulletin de la Soci{\'e}t{\'e} math{\'e}matique de France},
	Pages = {147--178},
	Title = {Sur l'ensemble des points de non-d{\'e}rivabilit{\'e} d'une fonction continue},
	Urldate = {2018-03-13},
	Volume = {2},
	Year = {1946}}

@article{SzeRiz04,
	Author = {G. Sz\'{e}kely and M. Rizzo},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {InterStat},
	Title = {Testing for Equal Distributions in High Dimension},
	Volume = {5},
	Year = {2004}}

@article{energy-distance,
	Author = {G. J. Sz{\'e}kely and M. L. Rizzo},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {InterStat},
	Number = {5},
	Title = {Testing for equal distributions in high dimensions},
	Year = {2004}}

@inproceedings{kfda,
	Archiveprefix = {arXiv},
	Author = {Harchaoui, Zaid and Bach, Francis R. and Moulines, \'Eric},
	Booktitle = {NIPS},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {0804.1026},
	Title = {Testing for Homogeneity with Kernel Fisher Discriminant Analysis},
	Year = {2008}}

@misc{cramer-gan,
	Archiveprefix = {arXiv},
	Author = {Bellemare, M. G. and Danihelka, I. and Dabney, W. and Mohamed, S. and Lakshminarayanan, B. and Hoyer, S. and Munos, R.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1705.10743},
	Title = {The {C}ramer Distance as a Solution to Biased {W}asserstein Gradients},
	Year = {2017}}

@article{dowson-landau,
	Author = {Dowson, D. C. and Landau, B. V.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Journal of Multivariate Analysis},
	Number = {3},
	Pages = {450--455},
	Title = {The {F}r{\'{e}}chet distance between multivariate normal distributions},
	Volume = {12},
	Year = {1982}}

@article{Piranian:1966,
	Author = {Piranian, G.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {The American Mathematical Monthly},
	Number = {4},
	Pages = {57--61},
	Title = {The {Set} of {Nondifferentiability} of a {Continuous} {Function}},
	Volume = {73},
	Year = {1966}}

@inproceedings{Zhang:2018,
	Archiveprefix = {arXiv},
	Author = {Zhang, Richard and Isola, Phillip and Efros, Alexei A. and Shechtman, Eli and Wang, Oliver},
	Booktitle = {CVPR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1801.03924},
	Title = {The Unreasonable Effectiveness of Deep Features as a Perceptual Metric},
	Year = {2018}}

@misc{Mityagin:2015,
	Archiveprefix = {arXiv},
	Author = {B. Mityagin},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1512.07276},
	Title = {The Zero Set of a Real Analytic Function},
	Year = {2015}}

@inproceedings{towards-principled-gans,
	Archiveprefix = {arXiv},
	Author = {Arjovsky, M. and Bottou, L.},
	Booktitle = {ICLR},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1701.04862},
	Title = {Towards Principled Methods for Training Generative Adversarial Networks},
	Year = {2017}}

@misc{anime-gans,
	Archiveprefix = {arXiv},
	Author = {Y. Jin and K. Zhang and M. Li and Y. Tian and H. Zhu and Z. Fang},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1708.05509},
	Title = {Towards the Automatic Anime Characters Creation with Generative Adversarial Networks},
	Year = {2017}}

@inproceedings{gen-mmd,
	Author = {Dziugaite, G. K. and Roy, D. M. and Ghahramani, Z.},
	Booktitle = {UAI},
	Title = {Training generative neural networks via Maximum Mean Discrepancy optimization},
	Year = {2015}}

@article{unbiased-convex,
	Author = {Bickel, P. J. and Lehmann, E. L.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {The Annals of Mathematical Statistics},
	Number = {5},
	Pages = {1523--1535},
	Title = {Unbiased Estimation in Convex Families},
	Volume = {40},
	Year = {1969}}

@article{SriFukLan11,
	Archiveprefix = {arXiv},
	Author = {B. K. Sriperumbudur and K. Fukumizu and G. R. G. Lanckriet},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1003.0887},
	Journal = {JMLR},
	Pages = {2389--2410},
	Title = {Universality, Characteristic Kernels and {RKHS} Embedding of Measures},
	Volume = {12},
	Year = {2011}}

@inproceedings{cyclegan,
	Archiveprefix = {arXiv},
	Author = {J.-Y. Zhu and T. Park and P. Isola and A. A. Efros},
	Booktitle = {ICCV},
	Eprint = {1703.10593},
	Title = {Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks},
	Year = {2017}}

@inproceedings{dcgan,
	Archiveprefix = {arXiv},
	Author = {Radford, A. and Metz, L. and Chintala, S.},
	Booktitle = {ICLR},
	Eprint = {1511.06434},
	Title = {Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks},
	Year = {2016}}

@book{diestel-uhl,
	Address = {Providence},
	Author = {Diestel, J. and Uhl, Jr, J. J.},
	Publisher = {American Mathematical Society},
	Title = {Vector Measures},
	Year = {1977}}

@inproceedings{wgan,
	Archiveprefix = {arXiv},
	Author = {Arjovsky, M. and Chintala, S. and Bottou, L.},
	Booktitle = {ICML},
	Eprint = {1701.07875},
	Title = {{W}asserstein Generative Adversarial Networks},
	Year = {2017}}

@misc{censored-normal,
	Author = {Sutherland, D. J.},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Howpublished = {Cross Validated answer},
	Title = {What are the mean and variance of a 0-censored multivariate normal?},
	Url = {https://stats.stackexchange.com/q/326347},
	Year = {2018},
	Bdsk-Url-1 = {https://stats.stackexchange.com/q/326347}}

@misc{Mescheder:2018,
	Archiveprefix = {arXiv},
	Author = {Mescheder, Lars and Geiger, Andreas and Nowozin, Sebastian},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Eprint = {1801.04406},
	Title = {Which Training Methods for {GANs} do actually Converge?},
	Year = {2018}}

@article{Villani:2004,
	Author = {Villani, Cedric},
	Journal = {Contemporary Mathematics},
	Pages = {95},
	Publisher = {Providence, RI: American Mathematical Society},
	Title = {Trend to equilibrium for dissipative equations, functional inequalities and mass transportation},
	Volume = {353},
	Year = {2004}}

@book{Villani:2009,
	Author = {Villani, C{\'e}dric},
	Publisher = {Springer Science \& Business Media},
	Title = {Optimal transport: old and new},
	Volume = {338},
	Year = {2008}}

@article{Oberman:2008,
	Author = {Adam M. Oberman},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {Proceedings of the American Mathematical Society},
	Title = {An Explicit Solution of the Lipschitz Extension Problem},
	Year = {2008}}

@article{Saidi:2009,
	Abstract = {Let \$G\$ be a compact subgroup of \$GL\_n({\textbackslash}R)\$ acting linearly on a finite dimensional vector space \$E\$. B. Malgrange has shown that the space \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty({\textbackslash}R{\textasciicircum}n,E){\textasciicircum}G\$ of \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty\$ and \$G\$-covariant functions is a finite module over the ring \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty({\textbackslash}R{\textasciicircum}n){\textasciicircum}G\$ of \${\textbackslash}mathcal\{C\}{\textasciicircum}{\textbackslash}infty\$ and \$G\$-invariant functions. First, we generalize this result for the Schwartz space \${\textbackslash}mathscr\{S\}({\textbackslash}R{\textasciicircum}n,E){\textasciicircum}G\$ of \$G\$-covariant functions. Secondly, we prove that any \$G\$-covariant distribution can be decomposed into a sum of \$G\$-invariant distributions multiplied with a fixed family of \$G\$-covariant polynomials. This gives a generalization of an Oksak result proved in ([O]).},
	Author = {Saidi, Anouar},
	Date-Added = {2019-04-02 12:33:53 +0000},
	Date-Modified = {2019-04-02 12:33:53 +0000},
	Journal = {arXiv:0902.1383 [math]},
	Keywords = {46F05, 58C46., 58C81, 58C99, Mathematics - Representation Theory},
	Month = feb,
	Note = {arXiv: 0902.1383},
	Title = {On covariant functions and distributions under the action of a compact group},
	Url = {http://arxiv.org/abs/0902.1383},
	Urldate = {2018-11-08},
	Year = {2009},
	Bdsk-Url-1 = {http://arxiv.org/abs/0902.1383}}

@article{Retherford:1978,
	Author = {Retherford, JR and others},
	Journal = {Bulletin of the American Mathematical Society},
	Number = {4},
	Pages = {681--685},
	Publisher = {American Mathematical Society},
	Title = {J. Diestel and JJ Uhl, Jr., Vector measures},
	Volume = {84},
	Year = {1978}}

@article{durmus2018analysis,
	Author = {Durmus, Alain and Majewski, Szymon and Miasojedow, B{\l}a{\.z}ej},
	Journal = {arXiv preprint arXiv:1802.09188},
	Title = {Analysis of Langevin Monte Carlo via convex optimization},
	Year = {2018}}

@article{bernton2018langevin,
	Author = {Bernton, Espen},
	Journal = {arXiv preprint arXiv:1802.08671},
	Title = {Langevin Monte Carlo and JKO splitting},
	Year = {2018}}

@article{gretton2012kernel,
	Author = {Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte J and Sch{\"o}lkopf, Bernhard and Smola, Alexander},
	Journal = {Journal of Machine Learning Research},
	Title = {A kernel two-sample test},
	Year = {2012}}


@article{wirnsbergertargetetNF2020,
	Author = {Wirnsberger,Peter and Ballard,Andrew J. and Papamakarios,George and Abercrombie,Stuart and Racani\`ere,Sebastien and Pritzel, Alexander and Rezende,Danilo and Blundell,Charles},
	Journal = {The Journal of Chemical Physics},
	Number = {14},
	Pages = {144112},
	Title = {Targeted free energy estimation via learned mappings},
	Volume = {153},
	Year = {2020}}

@article{wang2019accelerated,
  title={Accelerated information gradient flow},
  author={Wang, Yifei and Li, Wuchen},
  journal={arXiv preprint arXiv:1909.02102},
  year={2019}
}
@inproceedings{liu2019understanding,
  title={Understanding and accelerating particle-based variational inference},
  author={Liu, Chang and Zhuo, Jingwei and Cheng, Pengyu and Zhang, Ruiyi and Zhu, Jun},
  booktitle={International Conference on Machine Learning},
  pages={4082--4092},
  year={2019},
}

@inproceedings{zhu2020variance,
  title={Variance Reduction and Quasi-{N}ewton for Particle-Based Variational Inference},
  author={Zhu, Michael and Liu, Chang and Zhu, Jun},
  booktitle={International Conference on Machine Learning},
  pages={11576--11587},
  year={2020},
}

@article{reich2021fokker,
  title={Fokker--{P}lanck Particle Systems for {B}ayesian Inference: Computational Approaches},
  author={Reich, Sebastian and Weissmann, Simon},
  journal={SIAM/ASA Journal on Uncertainty Quantification},
  volume={9},
  number={2},
  pages={446--482},
  year={2021},
}

@article{pitt2012some,
  title={On some properties of {M}arkov chain {M}onte {C}arlo simulation methods based on the particle filter},
  author={Pitt, Michael K and dos Santos Silva, Ralph and Giordani, Paolo and Kohn, Robert},
  journal={Journal of Econometrics},
  volume={171},
  number={2},
  pages={134--151},
  year={2012},
  publisher={Elsevier}
}

@inproceedings{corenflos2021differentiable,
  title={Differentiable particle filtering via entropy-regularized optimal transport},
  author={Corenflos, Adrien and Thornton, James and Deligiannidis, George and Doucet, Arnaud},
  booktitle={International Conference on Machine Learning},
  year={2021},
}


@software{inferencegym2020,
  author = {Pavel Sountsov and Alexey Radul and contributors},
  title = {Inference Gym},
  url = {https://pypi.org/project/inference_gym},
  version = {0.0.4},
  year = {2020},
}

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  title={Classification of radar returns from the ionosphere using neural networks},
  author={Sigillito, Vincent G and Wing, Simon P and Hutton, Larrie V and Baker, Kile B},
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@article{meng2021estimating,
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  pages={25359--25369},
  year={2021}
}

@article{jing2013regularity,
  title={Regularity properties of viscosity solutions of integro-partial differential equations of Hamilton--Jacobi--Bellman type},
  author={Jing, Shuai},
  journal={Stochastic Processes and their Applications},
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  number={2},
  pages={300--328},
  year={2013},
  publisher={Elsevier}
}

@article{de2022convergence,
  title={Convergence of denoising diffusion models under the manifold hypothesis},
  author={De Bortoli, Valentin},
  journal={arXiv preprint arXiv:2208.05314},
  year={2022}
}


@article{gyongy1996existence,
  title={Existence of strong solutions for {I}t{\^o}'s stochastic equations via approximations},
  author={Gy{\"o}ngy, Istv{\'a}n and Krylov, Nicolai},
  journal={Probability theory and related fields},
  volume={105},
  number={2},
  pages={143--158},
  year={1996},
  publisher={Springer}
}

@book{oksendal2003stochastic,
  title={{Stochastic Differential Equations}},
  author={{\O}ksendal, Bernt},
  year={2003},
  publisher={Springer}
}

@article{gispenlamacraft2020ground,
  title={Ground states of quantum many body lattice models via reinforcement learning},
  author={Gispen, Willem and Lamacraft, Austen},
  journal={arXiv preprint arXiv:2012.07063},
  year={2020}
}


@article{ruiz2017particle,
  title={Particle smoothing for hidden diffusion processes: Adaptive path integral smoother},
  author={Ruiz, Hans-Christian and Kappen, Hilbert J},
  journal={IEEE Transactions on Signal Processing},
  volume={65},
  number={12},
  pages={3191--3203},
  year={2017},
  publisher={IEEE}
}

@inproceedings{lawson2018twisted,
  title={Twisted variational sequential {M}onte {C}arlo},
  author={Lawson, Dieterich and Tucker, George and Naesseth, Christian A and Maddison, Chris and Adams, Ryan P and Teh, Yee Whye},
  booktitle={Third workshop on Bayesian Deep Learning (NeurIPS)},
  year={2018}
}


@article{hartmann2019variational,
  title={Variational approach to rare event simulation using least-squares regression},
  author={Hartmann, Carsten and Kebiri, Omar and Neureither, Lara and Richter, Lorenz},
  journal={Chaos: An Interdisciplinary Journal of Nonlinear Science},
  volume={29},
  number={6},
  pages={063107},
  year={2019},
  publisher={AIP Publishing LLC}
}


@article{huang2021schrodinger,
  title={{S}chr{\"o}dinger-{F}{\"o}llmer sampler: {S}ampling without ergodicity},
  author={Huang, Jian and Jiao, Yuling and Kang, Lican and Liao, Xu and Liu, Jin and Liu, Yanyan},
  journal={arXiv preprint arXiv:2106.10880},
  year={2021}
}

@article{ruzayqat2022unbiased,
  title={Unbiased Estimation using a Class of Diffusion Processes},
  author={Ruzayqat, Hamza and Beskos, Alexandros and Crisan, Dan and Jasra, Ajay and Kantas, Nikolas},
  journal={arXiv preprint arXiv:2203.03013},
  year={2022}
}

@article{cattiaux2021time,
  title={Time reversal of diffusion processes under a finite entropy condition},
  author={Cattiaux, Patrick and Conforti, Giovanni and Gentil, Ivan and L{\'e}onard, Christian},
  journal={arXiv preprint arXiv:2104.07708},
  year={2021}
}


@article{tamar2016value,
  title={Value iteration networks},
  author={Tamar, Aviv and Wu, Yi and Thomas, Garrett and Levine, Sergey and Abbeel, Pieter},
  journal={Advances in neural information processing systems},
  volume={29},
  year={2016}
}
@article{fulop2021efficient,
  title={Efficient Likelihood-based Estimation via Annealing for Dynamic Structural Macrofinance Models},
  author={Fulop, Andras and Heng, Jeremy and Li, Junye},
  journal={Available at SSRN 3878869},
  year={2021}
}


@article{saremi2019neural,
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  year={2019}
}

@article{masreliez1977robust,
  title={Robust {B}ayesian estimation for the linear model and robustifying the {K}alman filter},
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@article{vono2022efficient,
  title={Efficient {MCMC} sampling with dimension-free convergence rate using {ADMM}-type splitting},
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  volume={23},
  number={25},
  year={2022},
}

@article{liang2022proximal,
  title={A Proximal Algorithm for Sampling},
  author={Liang, Jiaming and Chen, Yongxin},
  journal={arXiv preprint arXiv:2202.13975},
  year={2022}
}

@article{geffner2022langevin,
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  author={Geffner, Tomas and Domke, Justin},
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  year={2022}
}

@article{kappen2012optimal,
  title={Optimal control as a graphical model inference problem},
  author={Kappen, Hilbert J and G{\'o}mez, Vicen{\c{c}} and Opper, Manfred},
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  volume={87},
  number={2},
  pages={159--182},
  year={2012},
  publisher={Springer}
}

@article{dai1991stochastic,
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  number={1},
  pages={313--329},
  year={1991},
  publisher={Springer}
}

@article{liu2022let,
  title={Let us Build Bridges: Understanding and Extending Diffusion Generative Models},
  author={Liu, Xingchao and Wu, Lemeng and Ye, Mao and Liu, Qiang},
  journal={arXiv preprint arXiv:2208.14699},
  year={2022}
}

@article{tzen2019neural,
  title={Neural stochastic differential equations: Deep latent {G}aussian models in the diffusion limit},
  author={Tzen, Belinda and Raginsky, Maxim},
  journal={arXiv preprint arXiv:1905.09883},
  year={2019}
}

@inproceedings{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},
  booktitle={International Conference on Learning Representations},
  year={2018}
}

@article{follmer1984entropy,
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  pages={156--163},
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@article{ye2022first,
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}

@article{lee2022convergence,
  title={Convergence for score-based generative modeling with polynomial complexity},
  author={Lee, Holden and Lu, Jianfeng and Tan, Yixin},
  journal={arXiv preprint arXiv:2206.06227},
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@inproceedings{
vargas2023denoising,
title={Denoising Diffusion Samplers},
author={Francisco Vargas and Will Sussman Grathwohl and Arnaud Doucet},
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year={2023},
url={https://openreview.net/forum?id=8pvnfTAbu1f}
}
