%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DRO with Wasserstein: theory
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{yue2021linear,
  title={On linear optimization over {W}asserstein balls},
  author={Yue, Man-Chung and Kuhn, Daniel and Wiesemann, Wolfram},
  journal={Mathematical Programming},
  year={2021},
  publisher={Springer}
}

@inproceedings{ref:nguyen2019optimistic,
	title={Optimistic Distributionally Robust Optimization for Nonparametric Likelihood Approximation},
	author={Nguyen, Viet Anh and Shafieezadeh-Abadeh, Soroosh and Yue, Man-Chung and Kuhn, Daniel and Wiesemann, Wolfram},
	booktitle={Advances in Neural Information Processing Systems 32},
	year={2019}, 
	pages = {15872--15882},
}

@article{vu2022distributionally,
  title={Distributionally Robust Fair Principal Components via Geodesic Descents},
  author={Vu, Hieu and Tran, Toan and Yue, Man-Chung and Nguyen, Viet Anh},
  journal={arXiv preprint arXiv:2202.03071},
  year={2022}
}

@inproceedings{taskesen2021sequential,
  title={Sequential domain adaptation by synthesizing distributionally robust experts},
  author={Taskesen, Bahar and Yue, Man-Chung and Blanchet, Jose and Kuhn, Daniel and Nguyen, Viet Anh},
  booktitle={International Conference on Machine Learning},
  pages={10162--10172},
  year={2021},
  organization={PMLR}
}

@book{beck2017first,
  title={First-order Methods in Optimization},
  author={Beck, Amir},
  year={2017},
  publisher={SIAM}
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  author={Bonnans, J Fr{\'e}d{\'e}ric and Shapiro, Alexander},
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@article{ref:rippl2016limit,
	title={Limit laws of the empirical {W}asserstein distance: {G}aussian distributions},
	author={Rippl, T. and Munk, A. and Sturm, A.},
	journal={Journal of Multivariate Analysis},
	volume={151},
	pages={90--109},
	year={2016},
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@incollection{ref:bhagat2011node,
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@inproceedings{ref:bodendorf2009detecting,
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@article{ref:enev2016automobile,
  title={Automobile driver fingerprinting},
  author={Enev, Miro and Takakuwa, Alex and Koscher, Karl and Kohno, Tadayoshi},
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  number={1},
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@article{ref:zhu2014vehicle,
  title={Vehicle detection in driving simulation using extreme learning machine},
  author={Zhu, Wentao and Miao, Jun and Hu, Jiangbi and Qing, Laiyun},
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@article{ref:tomar2013survey,
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@inproceedings{ref:naraei2016application,
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  pages={848--852},
  year={2016},
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}
@article{ref:friedman2008sparse,
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  year={2012},
  publisher={MIT Press}
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@article{ref:ledoi2004well,
title = "A well-conditioned estimator for large-dimensional covariance matrices",
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number = "2",
pages = "365 - 411",
year = "2004",
author = "Olivier Ledoit and Michael Wolf",
}

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  title={Signals, Systems and Inference},
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  year={2015},
  publisher={Pearson}
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@book{ref:cover2012elements,
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@misc{Dua:2019,
author = "Dua, Dheeru and Graff, Casey",
year = "2017",
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@book{ref:mackay2003information,
  title={Information Theory, Inference and Learning Algorithms},
  author={D.J.C.~MacKay},
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@book{ref:wooldridge2010econometric,
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@book{ref:chatfield2016analysis,
  title={The Analysis of Time Series: {A}n Introduction},
  author={C.~Chatfield},
  year={2016},
  publisher={CRC Press}
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@book{ref:stock2015introduction,
  title={Introduction to Econometrics},
  author={J.H. Stock and M.W.~Watson},
  publisher={Prentice Hall},
  year={2015}
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@book{ref:ogata2009modern,
  title={Modern Control Engineering},
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@book{ref:golnaraghi2017automatic,
  title={Automatic Control Systems},
  author={F.~Golnaraghi and B.C.~Kuo},
  year={2017},
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}

@article{ref:chen2018drocc,
	title={Data-Driven Chance Constrained Programs over {W}asserstein Balls},
	author = {Chen, Z. and Kuhn, D. and Wiesemann, W.},
	journal={arXiv preprint arXiv:1809.00210},
	year={2018}
}

@article{ref:chen2018adaptive,
  title={Adaptive Robust Optimization with Scenario-wise Ambiguity Sets},
  author={Z.~Chen and M.~Sim and P.~Xiong},
  journal={Available from Optimization Online},
  year={2018}
}
@article{ref:bertsimas2018data,
  title={Data-driven Robust Optimization},
  author={Dimitris Bertsimas and Vishal Gupta and Nathan Kallus},
  journal={Mathematical Programming},
  volume={167},
  number={2},
  pages={235--292},
  year={2018},
  publisher={Springer}
}
@article{ref:bertsimas2018robust,
  title={Robust Sample Average Approximation},
  author={Dimitris Bertsimas and Vishal Gupta and Nathan Kallus},
  journal={Mathematical Programming},
  volume={171},
  number={1-2},
  pages={217--282},
  year={2018},
  publisher={Springer}
}

@article{ref:xie2018drocc,
	title={On Distributionally Robust Chance Constrained Program with {W}asserstein Distance},
	author = {Xie, W.},
	journal={arXiv preprint arXiv:1806.07418},
	year={2018}
}

@book{ref:villani2008optimal,
	title={Optimal Transport: Old and New},
	author={C.~Villani},
	year={2008},
	publisher={Springer Science \& Business Media}
}

@book{ref:rockafellar1997convex,
  title={Convex Analysis},
  author={R.T.~Rockafellar},
  year={1997},
  publisher={Princeton University Press}
}

@article{ref:blanchet2019inverse,
	title={Optimal Uncertainty Size in Distributionally Robust Inverse Covariance Estimation},
	author = {Blanchet, J. and Si, N.},
	journal={arXiv preprint arXiv:1901.07693},
	year={2019}
}

@article{ref:sturt2018data-driven,
	title={A Data-Driven Approach for Multi-Stage Linear Optimization},
	author={D. Bertsimas and S. Shtern and B. Sturt},
	journal={Available from Optimization Online},
	year={2018}
}

@article{ref:zhen2019distributionally,
  title={Distributionally robust nonlinear optimization},
  author={J.~Zhen and D.~Kuhn and W.~Wiesemann},
  journal={Working paper},
  year={2019}
}

@article{ref:zymler2013wcvar,
author = {Zymler, S. and Kuhn, D. and Rustem, B.},
title = {Worst-Case Value at Risk of Nonlinear Portfolios},
journal = {Management Science},
volume = {59},
number = {1},
pages = {172--188},
year = {2013}
}

@article{ref:el-ghaoui2003wcvar,
author = {El Ghaoui, L. and Oks, M. and Oustry, F.},
title = {Worst-Case Value-At-Risk and Robust Portfolio Optimization: A Conic Programming Approach},
journal = {Operations Research},
volume = {51},
number = {4},
pages = {543--556},
year = {2003}
}

@article{ref:natarajan2010utility,
  title={Tractable robust expected utility and risk models for portfolio optimisation},
  author={K. Natarajan and M. Sim and J. Uichanco},
  journal={Mathematical Finance},
  volume={20},
  number={4},
  pages={695--731},
 year={2010}
}

@article{ref:ben2015deriving,
  title={Deriving robust counterparts of nonlinear uncertain inequalities},
  author={A.~Ben-Tal and D.~Den Hertog and J.~P.~Vial},
  journal={Mathematical Programming},
  volume={149},
  number={1-2},
  pages={265--299},
  year={2015},
  publisher={Springer}
}

@article{ref:kantorovich1958space,
	title={On a space of totally additive functions},
	author={L.V.~Kantorovich and G.~Rubinshtein},
	journal={Vestnik Leningrad University},
	volume={13},
	number={7},
	pages={52--59},
	year={1958}
}

@article{ref:esfahani2018data,
	title={Data-driven distributionally robust optimization using the {W}asserstein metric: Performance guarantees and tractable reformulations},
	author={P.~{Mohajerin Esfahani} and D.~Kuhn},
	journal={Mathematical Programming},
	volume={171},
	number={1-2},
	pages={115--166},
	year={2018},
	publisher={Springer}
}

@article{ref:blanchet2019quantifying,
	title={Quantifying distributional model risk via optimal transport},
	author={J.~Blanchet and K.~Murthy},
	journal = {Mathematics of Operations Research},
    volume = {44},
    number = {2},
    pages = {565--600},
    year = {2019},
}

@article{ref:gao2016distributionally,
	title={Distributionally robust stochastic optimization with {W}asserstein distance},
	author={R.~Gao and A.~J.~Kleywegt},
	journal={arXiv preprint arXiv:1604.02199},
	year={2016}
}

@article{ref:wozabal2012framework,
	title={A framework for optimization under ambiguity},
	author={D.~Wozabal},
	journal={Annals of Operations Research},
	volume={193},
	number={1},
	pages={21--47},
	year={2012},
	publisher={Springer}
}

@article{ref:owhadi2017extreme,
	title={Extreme points of a ball about a measure with finite support},
	author={H.~Owhadi and C.~Scovel},
	journal={Communications in Mathematical Sciences},
	volume={15},
	number={1},
	pages={77--96},
	year={2017},
	publisher={International Press of Boston}
}

@article{ref:pflug2007ambiguity,
	title={Ambiguity in portfolio selection},
	author={G.~Pflug and D.~Wozabal},
	journal={Quantitative Finance},
	volume={7},
	number={4},
	pages={435--442},
	year={2007},
	publisher={Taylor \& Francis}
}

@article{ref:nguyen2019bridging,
	title={Bridging {B}ayesian and Minimax Mean Square Error Estimation via {W}asserstein Distributionally Robust Optimization},
	author={V.A. Nguyen and S. Shafieezadeh-Abadeh and D. Kuhn and P. {Mohajerin Esfahani}},
	journal={Working paper},
	year={2019}
}

@inproceedings{ref:monge1781memoire,
  author = {G.~Monge},
  booktitle= {Histoire de l'Acad{\'e}mie Royale des Sciences de Paris},
  pages = {666-704},
  title = {M{\'e}moire sur la th{\'e}orie des d{\'e}blais et des remblais},
  year = {1781}
}

@article{ref:kantorovich1942translocation,
	author = {L.V.~Kantorovich},
	year = {1942},
	pages = {199-201},
	title = {On the translocation of masses},
	journal = {Doklady Akademii Nauk USSR},
	volume = {37}
}

@article{ref:zhao2018data,
	title = {Data-driven risk-averse stochastic optimization with {W}asserstein metric},
	journal = "Operations Research Letters",
	volume = "46",
	number = "2",
	pages = "262 - 267",
	year = "2018",
	author = "C.~Zhao and Y.~Guan",
}

@article{ref:taskesen2019complexity,
	title =  {On the complexity of computing {W}asserstein distances},
	author = {B.~Ta\c skesen and S.~Shafieezadeh-Abadeh and D.~Kuhn},
	journal = {Working paper},
	year = {2019}
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Elliptical
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@book{ref:fang1990symmetric,
  author = {Fang, {Kai-Tai} and Kotz, {Samuel} and Ng, {Kai Wang}},
  publisher = {Chapman \& Hall},
  title = {Symmetric Multivariate and Related Distributions},
  year = 1990
}

@article{ref:cambanis1981theory,
	title={On the theory of elliptically contoured distributions},
	author={Cambanis, Stamatis and Huang, Steel and Simons, Gordon},
	journal={Journal of Multivariate Analysis},
	volume={11},
	number={3},
	pages={368--385},
	year={1981},
	publisher={Elsevier}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DRO with Wasserstein: applications
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



@article{ref:shapiro2021bayesian,
	title = {Bayesian {Distributionally} {Robust} {Optimization}},
	url = {http://arxiv.org/abs/2112.08625},
	publisher = {arXiv},
	author = {Shapiro, Alexander and Zhou, Enlu and Lin, Yifan},
	month = dec,
	year = {2021},
	note = {Number: arXiv:2112.08625
arXiv:2112.08625 [math]},
}

@misc{ref:garisch2019model,
	title = {Model lifecycle transformation: {How} banks are unlocking efficiencies},
	shorttitle = {Model lifecycle transformation},
	url = {https://financialservicesblog.accenture.com/model-lifecycle-transformation-how-banks-are-unlocking-efficiencies},
	abstract = {Learn how banks can transform the model lifecycle to improve the efficiency and effectiveness of activities across development, validation and governance functions.},
	language = {en-US},
	urldate = {2022-05-24},
	journal = {Financial Services Blog},
	publisher = {Accenture},
	author = {Garisch, Gordon and Merchant, Akber},
	month = apr,
	year = {2019},
	file = {Snapshot:C\:\\Users\\shrek\\Zotero\\storage\\MHHXLQPG\\model-lifecycle-transformation-how-banks-are-unlocking-efficiencies.html:text/html},
}


@inproceedings{ref:shafieezadeh2015distributionally,
	title={Distributionally robust logistic regression},
	author={S.~Shafieezadeh-Abadeh and P.~{Mohajerin Esfahani} and D.~Kuhn},
	booktitle={Advances in Neural Information Processing Systems 28},
	pages={1576--1584},
	year={2015}
}

@article{ref:shafieezadeh2017regularization,
	title={Regularization via mass transportation},
	author={S.~Shafieezadeh-Abadeh and D.~Kuhn and P.~{Mohajerin Esfahani}},
	journal={arXiv preprint arXiv:1710.10016},
	year={2017}
}

@article{ref:nguyen2018distributionally,
	title={Distributionally Robust Inverse Covariance Estimation: The {W}asserstein Shrinkage Estimator},
	author={V.A. Nguyen and D. Kuhn and P. {Mohajerin Esfahani}},
	journal={arXiv preprint arXiv:1805.07194},
	year={2018}
}

@inproceedings{ref:shafieezadeh2018wasserstein,
	title={{W}asserstein Distributionally Robust {K}alman Filtering},
	author={S.~Shafieezadeh-Abadeh and V.A.~Nguyen and D.~Kuhn and P.~{Mohajerin Esfahani}},
	booktitle={Advances in Neural Information Processing Systems 31},
	pages={8483-8492},
	year={2018}
}

@article{ref:esfahani2018inverse,
	title={Data-driven inverse optimization with imperfect information},
	author={P.~{Mohajerin Esfahani} and S.~Shafieezadeh-Abadeh and G.A.~Hanasusanto and D.~Kuhn},
	journal={Mathematical Programming},
	volume={167},
	number={1},
	pages={191--234},
	year={2018},
	publisher={Springer}
}

@article{ref:blanchet2016robust,
	title={Robust {W}asserstein profile inference and applications to machine learning},
	author={J.~Blanchet and Y.~Kang and K.~Murthy},
	journal={arXiv preprint arXiv:1610.05627},
	year={2016}
}

@article{ref:blanchet2016sample,
	title={Sample out-of-sample inference based on {W}asserstein distance},
	author={J.~Blanchet and Y.~Kang},
	journal={arXiv preprint arXiv:1605.01340},
	year={2016}
}

@article{ref:blanchet2017data,
	title={Data-driven Optimal Transport Cost Selection for Distributionally Robust Optimization},
	author={J.~Blanchet and Y.~Kang and F.~Zhang and K.~Murthy},
	journal={arXiv preprint arXiv:1705.07152},
	year={2017}
}

@article{ref:gao2017wasserstein,
	title={{W}asserstein distributional robustness and regularization in statistical learning},
	author={R.~Gao and X.~Chen and A.~J.~Kleywegt},
	journal={arXiv preprint arXiv:1712.06050},
	year={2017}
}

@Book{ref:schervish1995theory,
  author =	 {M. J. Schervish},
  title = 	 {{Theory of Statistics}},
  publisher = 	 {Springer},
  year = 	 {1995},
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@article{ref:chen2018data,
	title={Data-Driven Chance Constrained Programs over {W}asserstein Balls},
	author={Z.~Chen and D.~Kuhn and W.~Wiesemann},
	journal={arXiv preprint arXiv:1809.00210},
	year={2018}
}

@article{ref:cheng2018distributionally,
	title={Distributionally Robust Optimization with Principal Component Analysis},
	author={J.~Cheng and R.~Li-Yang Chen and H.~N.~Najm and A.~Pinar and C.~Safta and J.~Watson},
	journal={SIAM Journal on Optimization},
	volume={28},
	number={2},
	pages={1817--1841},
	year={2018},
	publisher={SIAM}
}

@article{ref:xie2018distributionally,
	title={On Distributionally Robust Chance Constrained Program with {W}asserstein Distance},
	author={W.~Xie},
	journal={arXiv preprint arXiv:1806.07418},
	year={2018}
}

@inproceedings{ref:gao2018robust,
	title={Robust Hypothesis Testing Using {W}asserstein Uncertainty Sets},
	author={R.~Gao and L.~Xie and Y.~Xie and H.~Xu},
	booktitle={Advances in Neural Information Processing Systems 31},
	pages = {7913--7923},
	year={2018}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DRO with Wasserstein: performance guarantee
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@inproceedings{ref:lee2017minimax,
	title={Minimax statistical learning with {W}asserstein distances},
	author={J.~Lee and M.~Raginsky},
	booktitle={Advances in Neural Information Processing Systems 31},
	pages = {2692--2701},
	year={2018}
}

@article{ref:fournier2015rate,
	title={On the rate of convergence in {W}asserstein distance of the empirical measure},
	author={N.~Fournier and A.~Guillin},
	journal={Probability Theory and Related Fields},
	volume={162},
	number={3-4},
	pages={707--738},
	year={2015},
	publisher={Springer}
}

@article{ref:weed2017sharp,
	title={Sharp asymptotic and finite-sample rates of convergence of empirical measures in {W}asserstein distance},
	author={J.~Weed and F.~Bach},
	journal={To appear in Bernoulli},
	year={2019}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Wasserstein in ML
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@article{ref:cuturi2014ground,
	title={Ground metric learning},
	author={M.~Cuturi and D.~Avis},
	journal={The Journal of Machine Learning Research},
	volume={15},
	number={1},
	pages={533--564},
	year={2014}
}

@article{ref:rubner2000earth,
	title={The earth mover's distance as a metric for image retrieval},
	author={Y.~Rubner and C.~Tomasi and L.~J.~Guibas},
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@article{ref:parikh2014proximal,
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	number={3},
	pages={127--239},
	year={2014},
	publisher={Now Publishers}
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@article{ref:courty2017optimal, 
	author={N.~Courty and R.~Flamary and D.~Tuia and A.~Rakotomamonjy}, 
	journal={IEEE Transactions on Pattern Analysis and Machine Intelligence}, 
	title={Optimal Transport for Domain Adaptation}, 
	year={2017}, 
	volume={39}, 
	number={9}, 
	pages={1853-1865}, 
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@article{ref:rujeerapaiboon2018scenario,
	author="N.~Rujeerapaiboon and K.~Schindler and D.~Kuhn and W.~Wiesemann",
	title="Scenario reduction revisited: fundamental limits and guarantees",
	journal="To appear in Mathematical Programming",
	year={2018}
	}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Wasserstein computation
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@article{ref:givens1984class,
	title={A class of {W}asserstein metrics for probability distributions},
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@article{ref:gelbrich1990formula,
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@article{ref:olkin1982distance,
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@article{ref:dowson1982frechet,
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	number={3},
	pages={450--455},
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@article{ref:peyre2019computational,
	title={Computational optimal transport},
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	volume={11},
	number={5-6},
	pages={355--607},
	year={2019},
	publisher={Now Publishers, Inc.}
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@book{ref:brualdi2006combinatorial,
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	author={R.A.~Brualdi},
	year={2006},
	publisher={Cambridge University Press}
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@book{ref:bertsekas1998network,
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@book{ref:bertsimas1997introduction,
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	publisher={Athena Scientific}
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@article{ref:bertsekas1981new,
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	publisher={Springer}
}

@article{ref:bertsekas1992auction,
	title={Auction algorithms for network flow problems: A tutorial introduction},
	author={D.P.~Bertsekas},
	journal={Computational Optimization and Applications},
	volume={1},
	number={1},
	pages={7--66},
	year={1992},
	publisher={Springer}
}

@inproceedings{ref:cuturi2013sinkhorn,
	title={Sinkhorn distances: Lightspeed computation of optimal transport},
	author={M.~Cuturi},
	booktitle={Advances in Neural Information Processing Systems 26},
	pages={2292--2300},
	year={2013}
}

@article{ref:essid2018quadratically,
	title={Quadratically regularized optimal transport on graphs},
	author={M.~Essid and J.~Solomon},
	journal={SIAM Journal on Scientific Computing},
	volume={40},
	number={4},
	pages={A1961--A1986},
	year={2018},
	publisher={SIAM}
}

@inproceedings{ref:muzellec2017tsallis,
	title={Tsallis Regularized Optimal Transport and Ecological Inference},
	author={B.~Muzellec and R.~Nock and G.~Patrini and F.~Nielsen},
	booktitle={Association for the Advancement of Artificial Intelligence},
	pages={2387--2393},
	year={2017}
}

@article{ref:benamou2015iterative,
	title={Iterative {B}regman projections for regularized transportation problems},
	author={J.~Benamou and G.~Carlier and M.~Cuturi and L.~Nenna and G.~Peyr{\'e}},
	journal={SIAM Journal on Scientific Computing},
	volume={37},
	number={2},
	pages={A1111--A1138},
	year={2015},
	publisher={SIAM}
}

@article{ref:schmitzer2016sparse,
	title={A sparse multiscale algorithm for dense optimal transport},
	author={B.~Schmitzer},
	journal={Journal of Mathematical Imaging and Vision},
	volume={56},
	number={2},
	pages={238--259},
	year={2016},
	publisher={Springer}
}

@article{ref:solomon2015convolutional,
	title={Convolutional {W}asserstein distances: Efficient optimal transportation on geometric domains},
	author={J.~Solomon and F.~De Goes and G.~Peyr{\'e} and M.~Cuturi and A.~Butscher and A.~Nguyen and T.~Du and L.~Guibas},
	journal={ACM Transactions on Graphics},
	volume={34},
	number={4},
	pages={66},
	year={2015},
	publisher={ACM}
}

@article{ref:peyre2017quantum,
	title={Quantum entropic regularization of matrix-valued optimal transport},
	author={G.~Peyr{\'e} and L.~Chizat and F.~Vialard and J.~Solomon},
	journal={European Journal of Applied Mathematics},
	pages={1--24},
	year={2017},
	publisher={Cambridge University Press}
}

@article{ref:peyre2015entropic,
	title={Entropic approximation of {W}asserstein gradient flows},
	author={G.~Peyr{\'e}},
	journal={SIAM Journal on Imaging Sciences},
	volume={8},
	number={4},
	pages={2323--2351},
	year={2015},
	publisher={SIAM}
}

@article{ref:karlsson2017generalized,
	title={Generalized {S}inkhorn iterations for regularizing inverse problems using optimal mass transport},
	author={J.~Karlsson and A.~Ringh},
	journal={SIAM Journal on Imaging Sciences},
	volume={10},
	number={4},
	pages={1935--1962},
	year={2017},
	publisher={SIAM}
}

@article{ref:chizat2018scaling,
	title={Scaling algorithms for unbalanced optimal transport problems},
	author={L.~Chizat and G.~Peyr{\'e} and B.~Schmitzer and F.~Vialard},
	journal={Mathematics of Computation},
	year={2018},
	volume = {87},
	pages = {2563-2609}
}

@inproceedings{ref:canas2012learning,
title = {Learning Probability Measures with respect to Optimal Transport Metrics},
author = {G.~Canas and L.~Rosasco},
booktitle = {Advances in Neural Information Processing Systems 25},
pages = {2492--2500},
year = {2012},
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%	Stability results
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{ref:dupacova1990stability,
	author="J.~Dupa{\v{c}}ov{\'a}",
	title="Stability and sensitivity-analysis for stochastic programming",
	journal="Annals of Operations Research",
	year="1990",
	volume="27",
	number="1",
	pages="115--142",
}

@article{ref:roemisch1991stability,
	author="W.~R{\"o}misch and R.~Schultz",
	title="Stability analysis for stochastic programs",
	journal="Annals of Operations Research",
	year="1991",
	volume="30",
	number="1",
	pages="241--266",
}

@book{ref:pflug2014multistage,
	title={Multistage Stochastic Optimization},
	author={G.~Pflug and A.~Pichler},
	year={2014},
	publisher={Springer}
}


@article{ref:roemisch2007stability,
author = {W.~R{\"o}misch and R.~Wets},
title = {Stability of $\varepsilon$-approximate Solutions to Convex Stochastic Programs},
journal = {SIAM Journal on Optimization},
volume = {18},
number = {3},
pages = {961-979},
year = {2007}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DRO with moments
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

@incollection{ref:scarf1958min,
	author={H.~Scarf},
	title={A min-max solution of an inventory problem},
	booktitle={Studies in the Mathematical Theory of Inventory and Production},
	publisher={Stanford University Press},
	year={1958},	
	pages={201--209},
	editor={Arrow, Kenneth Joseph and Karlin, Samuel and Scarf, Herbert}
}

@article{ref:delage2010distributionally,
	title={Distributionally robust optimization under moment uncertainty with application to data-driven problems},
	author={E.~Delage and Y.~Ye},
	journal={Operations Research},
	volume={58},
	number={3},
	pages={595--612},
	year={2010},
	publisher={INFORMS}
}

@article{ref:delage2010percentile,
  title={Percentile Optimization for {M}arkov Decision Processes with Parameter Uncertainty},
  author={Erick Delage and Shie Mannor},
  journal={Operations Research},
  year={2010},
  volume={58},
  pages={203-213}
}

@article{ref:goh2010distributionally,
	title={Distributionally robust optimization and its tractable approximations},
	author={J.~Goh and M.~Sim},
	journal={Operations Research},
	volume={58},
	number={4},
	pages={902--917},
	year={2010},
	publisher={INFORMS}
}

@article{ref:hanasusanto2015distributionally,
	title={Distributionally robust multi-item newsvendor problems with multimodal demand distributions},
	author={G.A.~Hanasusanto and D.~Kuhn and S.~W.~Wallace and S.~Zymler},
	journal={Mathematical Programming},
	volume={152},
	number={1-2},
	pages={1--32},
	year={2015},
	publisher={Springer}
}

@article{ref:vayanos2012constraint,
	title={A constraint sampling approach for multi-stage robust optimization},
	author={P.~Vayanos and D.~Kuhn and B.~Rustem},
	journal={Automatica},
	volume={48},
	number={3},
	pages={459--471},
	year={2012},
	publisher={Elsevier}
}


@incollection{ref:shapiro2001on,
	author={A.~Shapiro},
	title={On Duality Theory of Conic Linear Problems},
	booktitle={Semi-Infinite Programming},
	publisher={Kluwer Academic Publishers},
	year={2001},	
	pages={135--165},
}

@article{ref:ghaoui2003worst,
	title={Worst-case value-at-risk and robust portfolio optimization: {A} conic programming approach},
	author={L.~El Ghaoui and M.~Oks and F.~Oustry},
	journal={Operations Research},
	volume={51},
	number={4},
	pages={543--556},
	year={2003},
	publisher={INFORMS}
}
@article{ref:calafiore2007ambiguous,
author = {Calafiore, G.},
title = {Ambiguous Risk Measures and Optimal Robust Portfolios},
journal = {SIAM Journal on Optimization},
volume = {18},
number = {3},
pages = {853-877},
year = {2007},
}

@article{ref:calafiore2006distributionally,
	title={On distributionally robust chance-constrained linear programs},
	author={G.C.~Calafiore and L.~El Ghaoui},
	journal={Journal of Optimization Theory and Applications},
	volume={130},
	number={1},
	pages={1--22},
	year={2006},
	publisher={Springer}
}

@article{ref:calafiore2009parameter,
title = "Parameter estimation with expected and residual-at-risk criteria",
journal = "Systems \& Control Letters",
volume = "58",
number = "1",
pages = "39--46",
year = "2009",
author = "Giuseppe Calafiore and Ufuk Topcu and Laurent El Ghaoui",
}

@article{ref:chen2010cvar,
	title={From {CV}a{R} to uncertainty set: {I}mplications in joint chance-constrained optimization},
	author={W.~Chen and M.~Sim and J.~Sun and C.~Teo},
	journal={Operations Research},
	volume={58},
	number={2},
	pages={470--485},
	year={2010},
	publisher={INFORMS}
}

@article{ref:cheung2012linear,
	title={Linear matrix inequalities with stochastically dependent perturbations and applications to chance-constrained semidefinite optimization},
	author={S.~Cheung and A.~Man-Cho So and K.~Wang},
	journal={SIAM Journal on Optimization},
	volume={22},
	number={4},
	pages={1394--1430},
	year={2012},
	publisher={SIAM}
}

@article{ref:zymler2013distributionally,
	title={Distributionally robust joint chance constraints with second-order moment information},
	author={S.~Zymler and D.~Kuhn and B.~Rustem},
	journal={Mathematical Programming},
	volume={137},
	number={1-2},
	pages={167--198},
	year={2013},
	publisher={Springer}
}

@article{ref:bertsimas2010models,
	title={Models for minimax stochastic linear optimization problems with risk aversion},
	author={D.~Bertsimas and X.V.~Doan and K.~Natarajan and C.~Teo},
	journal={Mathematics of Operations Research},
	volume={35},
	number={3},
	pages={580--602},
	year={2010},
	publisher={INFORMS}
}

@article{ref:kuhn2011primal,
	title={Primal and dual linear decision rules in stochastic and robust optimization},
	author={D.~Kuhn and W.~Wiesemann and A.~Georghiou},
	journal={Mathematical Programming},
	volume={130},
	number={1},
	pages={177--209},
	year={2011},
	publisher={Springer}
}

@article{ref:hanasusanto2015perspective,
	title={A distributionally robust perspective on uncertainty quantification and chance constrained programming},
	author={G.A.~Hanasusanto and V.~Roitch and D.~Kuhn and W.~Wiesemann},
	journal={Mathematical Programming},
	volume={151},
	number={1},
	pages={35--62},
	year={2015},
	publisher={Springer}
}

@article{ref:rujeerapaiboon2015robust,
	title={Robust growth-optimal portfolios},
	author={N.~Rujeerapaiboon and D.~Kuhn and W.~Wiesemann},
	journal={Management Science},
	volume={62},
	number={7},
	pages={2090--2109},
	year={2015},
	publisher={Informs}
}

@article{ref:nguyen2019distributionally,
	title={Distributionally robust risk measures with structured {W}asserstein ambiguity sets},
	author = {V.A.~Nguyen and D.~Filipovic and D.~Kuhn},
	journal={Working paper},
	year={2019}
}

@article{ref:hanasusanto2016comment,
	title={A comment on ``computational complexity of stochastic programming problems''},
	author={G.A.~Hanasusanto and D.~Kuhn and W.~Wiesemann},
	journal={Mathematical Programming},
	volume={159},
	number={1-2},
	pages={557--569},
	year={2016},
	publisher={Springer}
}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% General DRO
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{ref:delage2019dicesion,
	title={{``Dice"-sion} Making under Uncertainty: When Can a Random Decision Reduce Risk?},
	author={E.~Delage and D.~Kuhn and W.~Wiesemann},
	journal={To appear in Management Science},
	year={2018}
}

@article{ref:vanparys2019optimal,
	title={From data to decisions: {D}istributionally robust optimization is optimal},
	author={B.~Van~Parys and P.~{Mohajerin Esfahani} and D.~Kuhn},
	journal={arXiv preprint arXiv:1704.04118},
	year={2017}
}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% General introduction
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@article{ref:michaud1989enigma,
	 author = {R.~Michaud},
	 journal = {Financial Analysts Journal},
	 number = {1},
	 pages = {31--42},
	 publisher = {CFA Institute},
	 title = {The {M}arkowitz Optimization Enigma: {I}s `Optimized' Optimal?},
	 volume = {45},
	 year = {1989}
}

@INCOLLECTION{ref:chopra2011errors,
	title = {The Effect of Errors in Means, Variances, and Covariances on Optimal Portfolio Choice},
	author = {V.~Chopra and W.~Ziemba},
	year = {2011},
	chapter = {18},
	pages = {249-257},
	booktitle = {The Kelly Capital Growth Investment Criterion: Theory and Practice},
	publisher = {World Scientific Publishing},
}

@article{ref:smith2006curse,
	author = {J.~Smith and R.~Winkler},
	title = {The Optimizer's Curse: {S}kepticism and Postdecision Surprise in Decision Analysis},
	journal = {Management Science},
	volume = {52},
	number = {3},
	pages = {311-322},
	year = {2006},
}

@book{ref:nesterov1994interior,
author = {Y.~Nesterov and A.~Nemirovskii},
title = {Interior-Point Polynomial Algorithms in Convex Programming},
publisher = {Society for Industrial and Applied Mathematics},
year = {1994},
}

@article{ref:kolouri2017optimal,
	title={Optimal mass transport: {S}ignal processing and machine-learning applications},
	author={S.~Kolouri and S.R.~Park and M.~Thorpe and D.~Slepcev and G.K.~Rohde},
	journal={IEEE Signal Processing Magazine},
	volume={34},
	number={4},
	pages={43--59},
	year={2017},
	publisher={IEEE}
}

@inproceedings{ref:murez2018image,
	title={Image to image translation for domain adaptation},
	author={Z.~Murez and S.~Kolouri and D.~Kriegman and R.~Ramamoorthi and K.~Kim},
	booktitle={IEEE Conference on Computer Vision and Pattern Recognition},
	pages={4500--4509},
	year={2018}
}

@article{ref:kundu2018discovery,
	title={Discovery and visualization of structural biomarkers from {MRI} using transport-based morphometry},
	author={S.~Kundu and S.~Kolouri and K.~I.~Erickson I and A.~F.~Kramer and E.~Mc{A}uley and G.K.~Rohde},
	journal={NeuroImage},
	volume={167},
	pages={256--275},
	year={2018},
	publisher={Elsevier}
}

@inproceedings{ref:arjovsky2017wasserstein,
	title={Wasserstein generative adversarial networks},
	author={M.~Arjovsky and S.~Chintala and L.~Bottou},
	booktitle={International Conference on Machine Learning},
	pages={214--223},
	year={2017}
}

@inproceedings{ref:gulrajani2017improved,
	title={Improved training of {W}asserstein {GAN}s},
	author={I.~Gulrajani and F.~Ahmed and M.~Arjovsky and V.~Dumoulin and A.~C.~Courville},
	booktitle={Advances in Neural Information Processing Systems 30},
	pages={5767--5777},
	year={2017}
}

@inproceedings{ref:genevay2018learning,
	title={Learning Generative Models with {S}inkhorn Divergences},
	author={A.~Genevay and G.~Peyr\'e and M.~Cuturi},
	booktitle={International Conference on Artificial Intelligence and Statistics},
	pages={1608--1617},
	year={2018}
}

@article{ref:flamary2018wasserstein,
	title={{W}asserstein discriminant analysis},
	author={R.~Flamary and M.~Cuturi and N.~Courty and A.~Rakotomamonjy},
	journal={Machine Learning},
	volume={107},
	number={12},
	pages={1923--1945},
	year={2018},
	publisher={Springer}
}

@inproceedings{ref:seguy2015principal,
	title={Principal geodesic analysis for probability measures under the optimal transport metric},
	author={V.~Seguy and M.~Cuturi},
	booktitle={Advances in Neural Information Processing Systems 28},
	pages={3312--3320},
	year={2015}
}

@inproceedings{ref:rolet2016fast,
	title={Fast dictionary learning with a smoothed {W}asserstein loss},
	author={A.~Rolet and M.~Cuturi and G.~Peyr{\'e}},
	booktitle={International Conference on Artificial Intelligence and Statistics},
	pages={630--638},
	year={2016}
}

@article{ref:schmitz2018wasserstein,
	title={Wasserstein dictionary learning: {O}ptimal transport-based unsupervised nonlinear dictionary learning},
	author={M.A.~Schmitz and M.~Heitz and N.~Bonneel and F.~Ngole and D.~Coeurjolly and M.~Cuturi and G.~Peyr{\'e} and J.~Starck},
	journal={SIAM Journal on Imaging Sciences},
	volume={11},
	number={1},
	pages={643--678},
	year={2018},
	publisher={SIAM}
}

@inproceedings{ref:ho2017multilevel,
	title={Multilevel clustering via {W}asserstein means},
	author={N.~Ho and X.~Nguyen and M.~Yurochkin and H.~H.~Bui and V.~Huynh and D.~Phung},
	booktitle={International Conference on Machine Learning},
	pages={1501--1509},
	year={2017}
}

@article{ref:nguyen2013convergence,
	title={Convergence of latent mixing measures in finite and infinite mixture models},
	author={Nguyen, X.},
	journal={The Annals of Statistics},
	volume={41},
	number={1},
	pages={370--400},
	year={2013}
}

@inproceedings{ref:kolouri2018sliced,
	title={Sliced {W}asserstein distance for learning {G}aussian mixture models},
	author={S.~Kolouri and G.K.~Rohde and H.~Hoffmann},
	booktitle={IEEE Conference on Computer Vision and Pattern Recognition},
	pages={3427--3436},
	year={2018}
}
@inproceedings{ref:kolouri2015transport,
	title={Transport-based single frame super resolution of very low resolution face images},
	author={S.~Kolouri and G.K.~Rohde},
	booktitle={IEEE Conference on Computer Vision and Pattern Recognition},
	pages={4876--4884},
	year={2015}
}

@article{ref:thorpe2017transportation,
	title={A Transportation ${L}^p$ Distance for Signal Analysis},
	author={M.~Thorpe and S.~Park and S.~Kolouri and G.K.~Rohde and D.~Slep{\v{c}}ev},
	journal={Journal of Mathematical Imaging and Vision},
	volume={59},
	number={2},
	pages={187--210},
	year={2017}
}

@inproceedings{ref:alvarez2018structured,
	title={Structured Optimal Transport},
	author={D.~Alvarez-Melis and T.~Jaakkola and S.~Jegelka},
	booktitle={International Conference on Artificial Intelligence and Statistics},
	pages={1771--1780},
	year={2018}
}

@inproceedings{ref:staib2019distributionally,
title = {Distributionally Robust Optimization and Generalization in Kernel Methods},
author = {Staib, Matthew and Jegelka, Stefanie},
booktitle = {Advances in Neural Information Processing Systems 32},
pages = {9134--9144},
year = {2019}
}


@inproceedings{ref:feydy2017optimal,
	title={Optimal transport for diffeomorphic registration},
	author={J.~Feydy and B.~Charlier and F.~Vialard and G.~Peyr{\'e}},
	booktitle={International Conference on Medical Image Computing and Computer-Assisted Intervention},
	pages={291--299},
	year={2017}
}

@article{ref:tartavel2016wasserstein,
	title={Wasserstein loss for image synthesis and restoration},
	author={G.~Tartavel and G.~Peyr{\'e} and Y.~Gousseau},
	journal={SIAM Journal on Imaging Sciences},
	volume={9},
	number={4},
	pages={1726--1755},
	year={2016},
	publisher={SIAM}
}

@article{ref:ferradans2014regularized,
	title={Regularized discrete optimal transport},
	author={S.~Ferradans and N.~Papadakis and G.~Peyr{\'e} and J.~Aujol},
	journal={SIAM Journal on Imaging Sciences},
	volume={7},
	number={3},
	pages={1853--1882},
	year={2014},
	publisher={SIAM}
}

@article{ref:papadakis2017convex,
	title={Convex Histogram-Based Joint Image Segmentation with Regularized Optimal Transport Cost},
	author={N.~Papadakis and J.~Rabin},
	journal={Journal of Mathematical Imaging and Vision},
	volume={59},
	number={2},
	pages={161--186},
	year={2017},
	publisher={Springer}
}

@article{ref:cazelles2018geodesic,
	title={Geodesic {PCA} versus Log-{PCA} of Histograms in the {W}asserstein Space},
	author={E.~Cazelles and V.~Seguy and J.~Bigot and M.~Cuturi and N.~Papadakis},
	journal={SIAM Journal on Scientific Computing},
	volume={40},
	number={2},
	pages={B429--B456},
	year={2018},
	publisher={SIAM}
}

@article{ref:wang2011optimal,
	title={An optimal transportation approach for nuclear structure-based pathology},
	author={W.~Wang and J.~A.~Ozolek and D.~Slepcev and A.~B.~Lee and C.~Chen and G.K.~Rohde},
	journal={IEEE Transactions on Medical Imaging},
	volume={30},
	number={3},
	pages={621--631},
	year={2011}
}

@inproceedings{ref:pele2008linear,
	title={A linear time histogram metric for improved sift matching},
	author={O.~Pele and M.~Werman},
	booktitle={European Conference on Computer Vision},
	pages={495--508},
	year={2008}
}

@inproceedings{ref:pele2009fast,
	title={Fast and robust earth mover's distances},
	author={O.~Pele and M.~Werman},
	booktitle={International Conference on Computer Vision},
	volume={9},
	pages={460--467},
	year={2009}
}

@article{ref:solomon2014earth,
	title={Earth mover's distances on discrete surfaces},
	author={J.~Solomon and R.~Rustamov and L.~Guibas and A.~Butscher},
	journal={ACM Transactions on Graphics},
	volume={33},
	number={4},
	pages={67},
	year={2014}
}


%%%%%%%%%%%%%%%%%%%%%%
% convex optimization
%%%%%%%%%%%%%%%%%%%%%%
@book{ref:boyd2004convex,
	title={Convex Optimization},
	author={S.~Boyd and L.~Vandenberghe},
	year={2004},
	publisher={Cambridge University Press}
}

@incollection{ref:yu2009projection,
title = {A General Projection Property for Distribution Families},
author = {Yu, Yao-liang and Li, Yuxi and Schuurmans, Dale and Csaba Szepesv\'{a}ri},
booktitle = {Advances in Neural Information Processing Systems 22},
pages = {2232--2240},
year = {2009},
}

@article{ref:popescu2007robust,
author = {Popescu, Ioana},
title = {Robust Mean-Covariance Solutions for Stochastic Optimization},
journal = {Operations Research},
volume = {55},
number = {1},
pages = {98-112},
year = {2007},
}



@book{ref:cohn2013measure,
  author = {Cohn, Donald L.},
  publisher = {Springer},
  title = {Measure Theory},
  year = 2013
}

@book{ref:berge1963topological,
	title={Topological Spaces: Including a Treatment of Multi-Valued Functions, Vector Spaces, and Convexity},
	author={Berge, C.},
	year={1963},
	publisher={Courier Corporation},
}

@Book{ref:hespanha2009linear,
  author =       {Jo{\~a}o P. Hespanha},
  title =        {Linear Systems Theory},
  publisher =    {Princeton University Press},
  year =         2009,
}

@article{ref:bertsimas2003shortfall,
  title={{Shortfall as a risk measure: Properties, optimization and applications}},
  author={Dimitris Bertsimas and Geoffrey J. Lauprete and Alexander Samarov},
  year={2004},
  journal = {Journal of Economic Dynamics \& Control},
  pages={1353-1381},
  volume = 28
}

@article{ref:sion1958minimax,
  author = {Sion, Maurice},
  journal = {Pacific Journal of Mathematics},
  number = 1,
  pages = {171--176},
  title = {On general minimax theorems},
  volume = 8,
  year = 1958
}

@book{ref:aliprantis06hitchhiker,
  author = {Aliprantis, Charalambos D. and Border, Kim C.},
  publisher = {Springer},
  title = {Infinite Dimensional Analysis: a Hitchhiker's Guide},
  year = 2006
}

@Article{ref:isii1960extrema,
  author={Keiiti Isii},
  title={{The extrema of probability determined by generalized moments (i) bounded random variables}},
  journal={Annals of the Institute of Statistical Mathematics},
  year=1960,
  volume={12},
  number={2},
  pages={119-134}
}

@article{ref:lobo1998socp,
title = "Applications of second-order cone programming",
journal = "Linear Algebra and its Applications",
volume = "284",
number = "1",
pages = "193 - 228",
year = "1998",
issn = "0024-3795",
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% Risk measure
%%%%%%%%%%%%%%%%%%%%%%

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@misc{ref:kaggle2011give,
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@inproceedings{
ref:bui2022counterfactual,
title={Counterfactual Plans under Distributional Ambiguity},
author={Ngoc Bui and Duy Nguyen and Viet Anh Nguyen},
booktitle={International Conference on Learning Representations},
year={2022},
}