Distributional robustness in inference

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.


Blanchet, Jose, Lin Chen, and Xun Yu Zhou. 2018. β€œDistributionally Robust Mean-Variance Portfolio Selection with Wasserstein Distances.” arXiv:1802.04885 [Stat], February.
Blanchet, Jose, Yang Kang, and Karthyek Murthy. 2016. β€œRobust Wasserstein Profile Inference and Applications to Machine Learning.” arXiv:1610.05627 [Math, Stat], October.
Blanchet, Jose, Yang Kang, Fan Zhang, and Karthyek Murthy. 2017. β€œData-Driven Optimal Cost Selection for Distributionally Robust Optimization.” arXiv:1705.07152 [Stat], May.
Blanchet, Jose, Karthyek Murthy, and Nian Si. 2019. β€œConfidence Regions in Wasserstein Distributionally Robust Estimation.” arXiv:1906.01614 [Math, Stat], June.
Blanchet, Jose, Karthyek Murthy, and Fan Zhang. 2018. β€œOptimal 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. β€œDistributionally 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. β€œBeing Robust (in High Dimensions) Can Be Practical.” arXiv:1703.00893 [Cs, Math, Stat], March.
Farokhi, Farhad. 2020. β€œDistributionally-Robust Machine Learning Using Locally Differentially-Private Data.” arXiv:2006.13488 [Cs, Math, Stat], June.
Gao, Rui, and Anton J. Kleywegt. 2022. β€œDistributionally Robust Stochastic Optimization with Wasserstein Distance.” arXiv.
Go, Jinwoo, and Tobin Isaac. n.d. β€œRobust Expected Information Gain for Optimal Bayesian Experimental Design Using Ambiguity Sets,” 10.
Husain, Hisham. 2020. β€œDistributional Robustness with IPMs and Links to Regularization and GANs.” arXiv:2006.04349 [Cs, Stat], June.
Mahdian, Saied, Jose Blanchet, and Peter Glynn. 2019. β€œOptimal Transport Relaxations with Application to Wasserstein GANs.” arXiv:1906.03317 [Cs, Math, Stat], June.
Meinshausen, Nicolai. 2018. β€œCausality from a Distributional Robustness Point of View.” In 2018 IEEE Data Science Workshop (DSW), 6–10.
Mohajerin Esfahani, Peyman, and Daniel Kuhn. 2018. β€œData-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. β€œLearning While Respecting Privacy and Robustness to Distributional Uncertainties and Adversarial Data.” arXiv:2007.03724 [Cs, Eess, Math], July.
Shapiro, Alexander. 2017. β€œDistributionally Robust Stochastic Programming.” SIAM Journal on Optimization 27 (4): 2258–75.
Shapiro, Alexander, Enlu Zhou, and Yifan Lin. 2021. β€œBayesian Distributionally Robust Optimization.” arXiv.
Weichwald, Sebastian, and Jonas Peters. 2020. β€œCausality in Cognitive Neuroscience: Concepts, Challenges, and Distributional Robustness.” arXiv:2002.06060 [q-Bio, Stat], July.

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