Placeholder, for inference which is robust to a mis=specification of distribution up to some ball in some probaility metric. I saw Jose Blanchet present on Wasserstein distributional robustness at MCM 2019. Bookmarked for later.
To understand: Connections to causal inference, differential privacy, adversarial learning, hedging in portfolios…
Also to understand: How old is distributional robustness? I feel like when I discovered this literature it was already old, but no-one seems to agree upon a specific foundational publication.
References
Blanchet, Jose, Lin Chen, and Xun Yu Zhou. 2018. “Distributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances.” arXiv:1802.04885 [Stat], February.
Blanchet, Jose, Yang Kang, and Karthyek Murthy. 2016. “Robust Wasserstein Profile Inference and Applications to Machine Learning.” arXiv:1610.05627 [Math, Stat], October.
Blanchet, Jose, Yang Kang, Fan Zhang, and Karthyek Murthy. 2017. “Data-Driven Optimal Cost Selection for Distributionally Robust Optimization.” arXiv:1705.07152 [Stat], May.
Blanchet, Jose, Karthyek Murthy, and Nian Si. 2019. “Confidence Regions in Wasserstein Distributionally Robust Estimation.” arXiv:1906.01614 [Math, Stat], June.
Blanchet, Jose, Karthyek Murthy, and Fan Zhang. 2018. “Optimal Transport Based Distributionally Robust Optimization: Structural Properties and Iterative Schemes.” arXiv:1810.02403 [Math], October.
Cisneros-Velarde, Pedro, Alexander Petersen, and Sang-Yun Oh. 2020. “Distributionally Robust Formulation and Model Selection for the Graphical Lasso.” In International Conference on Artificial Intelligence and Statistics, 756–65. PMLR.
Diakonikolas, Ilias, Gautam Kamath, Daniel M. Kane, Jerry Li, Ankur Moitra, and Alistair Stewart. 2017. “Being Robust (in High Dimensions) Can Be Practical.” arXiv:1703.00893 [Cs, Math, Stat], March.
Farokhi, Farhad. 2020. “Distributionally-Robust Machine Learning Using Locally Differentially-Private Data.” arXiv:2006.13488 [Cs, Math, Stat], June.
Gao, Rui, and Anton J. Kleywegt. 2022. “Distributionally Robust Stochastic Optimization with Wasserstein Distance.” arXiv.
Go, Jinwoo, and Tobin Isaac. n.d. “Robust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets,” 10.
Husain, Hisham. 2020. “Distributional Robustness with IPMs and Links to Regularization and GANs.” arXiv:2006.04349 [Cs, Stat], June.
Mahdian, Saied, Jose Blanchet, and Peter Glynn. 2019. “Optimal Transport Relaxations with Application to Wasserstein GANs.” arXiv:1906.03317 [Cs, Math, Stat], June.
Meinshausen, Nicolai. 2018. “Causality from a Distributional Robustness Point of View.” In 2018 IEEE Data Science Workshop (DSW), 6–10.
Mohajerin Esfahani, Peyman, and Daniel Kuhn. 2018. “Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations.” Mathematical Programming 171 (1): 115–66.
Sadeghi, Alireza, Gang Wang, Meng Ma, and Georgios B. Giannakis. 2020. “Learning While Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data.” arXiv:2007.03724 [Cs, Eess, Math], July.
Shapiro, Alexander. 2017. “Distributionally Robust Stochastic Programming.” SIAM Journal on Optimization 27 (4): 2258–75.
Shapiro, Alexander, Enlu Zhou, and Yifan Lin. 2021. “Bayesian Distributionally Robust Optimization.” arXiv.
Weichwald, Sebastian, and Jonas Peters. 2020. “Causality in Cognitive Neuroscience: Concepts, Challenges, and Distributional Robustness.” arXiv:2002.06060 [q-Bio, Stat], July.
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