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Distributionally robust optimization (DRO) has become a powerful framework for estimation under uncertainty, offering strong out-of-sample performance and principled regularization.
Confidence regions in Wasserstein distributionally robust estimation
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Observed universality of phase transitions in high-dimensional geometry, with implications for modern data analysis and signal processing
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On Milman’s inequality and random subspaces which escape through a mesh in ℝ \mathbb{R} n
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Asymptotics for least absolute deviation regression estimators
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Analysis of representations for domain adaptation
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Near-optimal signal recovery from random projections: Universal encoding strategies?
E. J. Candes and T. Tao · 2006
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Direct importance estimation with model selection and its application to covariate shift adaptation
M. Sugiyama, S. Nakajima, H. Kashima, P. Buenau, and M. Kawanabe · 2007
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Variational Analysis , volume 317
R. T. Rockafellar and R. J.-B. Wets · 2009
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Various thresholds for ℓ 1 \ell_{1} -optimization in compressed sensing
M. Stojnic · 2009
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Asymptotic behavior of adversarial training in binary classification
H. Taheri, R. Pedarsani, and C. Thrampoulidis · 2010
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The LASSO risk for gaussian matrices
M. Bayati and A. Montanari · 2011
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The noise-sensitivity phase transition in compressed sensing
D. L. Donoho, A. Maleki, and A. Montanari · 2011
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Robust statistics
P. J. Huber · 2011
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Optimal M-estimation in high-dimensional regression
D. Bean, P. J. Bickel, N. El Karoui, and B. Yu · 2013
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Robust solutions of optimization problems affected by uncertain probabilities
A. Ben-Tal, D. Den Hertog, A. De Waegenaere, B. Melenberg, and G. Rennen · 2013
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N. E. Karoui · 2013
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Hessian Schatten-norm regularization for linear inverse problems
S. Lefkimmiatis, J. P. Ward, and M. Unser · 2013
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The squared-error of generalized LASSO: A precise analysis
S. Oymak, C. Thrampoulidis, and B. Hassibi · 2013
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A framework to characterize performance of LASSO algorithms
M. Stojnic · 2013
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Intriguing properties of neural networks
C. Szegedy, W. Zaremba, I. Sutskever, J. Bruna, D. Erhan, I. Goodfellow, and R. Fergus · 2013
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Living on the edge: Phase transitions in convex programs with random data
D. Amelunxen, M. Lotz, M. B. McCoy, and J. A. Tropp · 2014
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Variance estimation in high-dimensional linear models
L. H. Dicker · 2014
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Explaining and harnessing adversarial examples
I. J. Goodfellow, J. Shlens, and C. Szegedy · 2014
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Universality in polytope phase transitions and message passing algorithms
M. Bayati, M. Lelarge, and A. Montanari · 2015
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On the rate of convergence in Wasserstein distance of the empirical measure
N. Fournier and A. Guillin · 2015
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A unified gradient regularization family for adversarial examples
C. Lyu, K. Huang, and H.-N. Liang · 2015
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Distributionally robust logistic regression
S. Shafieezadeh-Abadeh, P. Mohajerin Esfahani, and D. Kuhn · 2015
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Isotropically random orthogonal matrices: Performance of LASSO and minimum conic singular values
C. Thrampoulidis and B. Hassibi · 2015
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Statistical mechanics of optimal convex inference in high dimensions
M. Advani and S. Ganguli · 2016
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Sample out-of-sample inference based on Wasserstein distance
J. Blanchet and Y. Kang · 2016
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Maximum likelihood for variance estimation in high-dimensional linear models
L. H. Dicker and M. A. Erdogdu · 2016
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High dimensional robust M-estimation: Asymptotic variance via approximate message passing
D. Donoho and A. Montanari · 2016
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A minimax approach to supervised learning
F. Farnia and D. Tse · 2016
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Robust sensitivity analysis for stochastic systems
H. Lam · 2016
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DeepFool: a simple and accurate method to fool deep neural networks
S.-M. Moosavi-Dezfooli, A. Fawzi, and P. Frossard · 2016
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Stochastic gradient methods for distributionally robust optimization with f-divergences
H. Namkoong and J. C. Duchi · 2016
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Sharp MSE bounds for proximal denoising
S. Oymak and B. Hassibi · 2016
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Improved training of Wasserstein GANs
I. Gulrajani, F. Ahmed, M. Arjovsky, V. Dumoulin, and A. Courville · 2017
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Formal guarantees on the robustness of a classifier against adversarial manipulation
M. Hein and M. Andriushchenko · 2017
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Asymptotic behavior of support vector machine for spiked population model
H. Huang · 2017
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Eigenprism: inference for high dimensional signal-to-noise ratios
L. Janson, R. F. Barber, and E. Candes · 2017
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Towards deep learning models resistant to adversarial attacks
A. Madry, A. Makelov, L. Schmidt, D. Tsipras, and A. Vladu · 2017
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Gradient descent GAN optimization is locally stable
V. Nagarajan and J. Z. Kolter · 2017
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Unifying adversarial training algorithms with data gradient regularization
A. G. Ororbia II, D. Kifer, and C. L. Giles · 2017
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A universal analysis of large-scale regularized least squares solutions
A. Panahi and B. Hassibi · 2017
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Stabilizing training of generative adversarial networks through regularization
K. Roth, A. Lucchi, S. Nowozin, and T. Hofmann · 2017
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Distributionally robust stochastic programming
A. Shapiro · 2017
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Distributionally robust deep learning as a generalization of adversarial training
M. Staib and S. Jegelka · 2017
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Gradient regularization improves accuracy of discriminative models
High-dimensional dynamics of generalization error in neural networks
M. S. Advani, A. M. Saxe, and H. Sompolinsky · 2020
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Robust uncertainty sensitivity analysis
D. Bartl, S. Drapeau, J. Obloj, and J. Wiesel · 2020
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Benign overfitting in linear regression
P. L. Bartlett, P. M. Long, G. Lugosi, and A. Tsigler · 2020
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Two models of double descent for weak features
M. Belkin, D. Hsu, and J. Xu · 2020
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The phase transition for the existence of the maximum likelihood estimate in high-dimensional logistic regression
E. J. Candès and P. Sur · 2020
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D. Varga, A. Csiszárik, and Z. Zombori · 2017
Cited alongside, same era.
To understand deep learning we need to understand kernel learning
M. Belkin, S. Ma, and S. Mandal · 2018
Cited alongside, same era.
J. Blanchet, K. Murthy, and F. Zhang · 2018
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Gradient descent provably optimizes over-parameterized neural networks
S. S. Du, X. Zhai, B. Poczos, and A. Singh · 2018
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On the impact of predictor geometry on the performance on high-dimensional ridge-regularized generalized robust regression estimators
N. El Karoui · 2018
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Lipschitz regularized deep neural networks generalize and are adversarially robust
C. Finlay, J. Calder, B. Abbasi, and A. Oberman · 2018
Cited alongside, same era.
Neural tangent kernel: Convergence and generalization in neural networks
A. Jacot, F. Gabriel, and C. Hongler · 2018
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E. Dobriban, H. Hassani, D. Hong, and A. Robey · 2020
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Adversarial distributional training for robust deep learning
Y. Dong, Z. Deng, T. Pang, J. Zhu, and H. Su · 2020
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Learning models with uniform performance via distributionally robust optimization
J. Duchi and H. Namkoong · 2020
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Generalization error of generalized linear models in high dimensions
M. Emami, M. Sahraee-Ardakan, P. Pandit, S. Rangan, and A. Fletcher · 2020
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R. Gao · 2020
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Wasserstein distributionally robust optimization and variation regularization
R. Gao, X. Chen, and A. J. Kleywegt · 2020
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C. Gerbelot, A. Abbara, and F. Krzakala · 2020
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Universality laws for high-dimensional learning with random features
H. Hu and Y. M. Lu · 2020
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Precise statistical analysis of classification accuracies for adversarial training
A. Javanmard and M. Soltanolkotabi · 2020
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Precise tradeoffs in adversarial training for linear regression
A. Javanmard, M. Soltanolkotabi, and H. Hassani · 2020
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Analytic study of double descent in binary classification: The impact of loss
G. R. Kini and C. Thrampoulidis · 2020
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Principled learning method for Wasserstein distributionally robust optimization with local perturbations
Y. Kwon, W. Kim, J.-H. Won, and M. C. Paik · 2020
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The role of regularization in classification of high-dimensional noisy gaussian mixture
F. Mignacco, F. Krzakala, Y. Lu, P. Urbani, and L. Zdeborova · 2020
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Harmless interpolation of noisy data in regression
V. Muthukumar, K. Vodrahalli, V. Subramanian, and A. Sahai · 2020
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Adversarial risk via optimal transport and optimal couplings
M. S. Pydi and V. Jog · 2020
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The performance analysis of generalized margin maximizers on separable data
F. Salehi, E. Abbasi, and B. Hassibi · 2020
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Opportunities and challenges in deep learning adversarial robustness: A survey
S. H. Silva and P. Najafirad · 2020
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A general framework for optimal data-driven optimization
T. Sutter, B. P. Van Parys, and D. Kuhn · 2020
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Stronger and faster Wasserstein adversarial attacks
K. Wu, A. Wang, and Y. Yu · 2020
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Deep learning: a statistical viewpoint
P. L. Bartlett, A. Montanari, and A. Rakhlin · 2021
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Learning and decision-making with data: Optimal formulations and phase transitions
M. Bennouna and B. P. Van Parys · 2021
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Statistics of robust optimization: A generalized empirical likelihood approach
J. C. Duchi, P. W. Glynn, and H. Namkoong · 2021
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Scaleable input gradient regularization for adversarial robustness
C. Finlay and A. M. Oberman · 2021
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On the precise error analysis of support vector machines
A. Kammoun and M.-S. AlouiniFellow · 2021
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Internal Wasserstein distance for adversarial attack and defense
J. Li, J. Cao, S. Zhang, Y. Xu, J. Chen, and M. Tan · 2021
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Fundamental tradeoffs in distributionally adversarial training
M. Mehrabi, A. Javanmard, R. A. Rossi, A. Rao, and T. Mai · 2021
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The curious case of adversarially robust models: More data can help, double descend, or hurt generalization
Y. Min, L. Chen, and A. Karbasi · 2021
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The distribution of the LASSO: Uniform control over sparse balls and adaptive parameter tuning
L. Miolane and A. Montanari · 2021
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Fundamental limits of ridge-regularized empirical risk minimization in high dimensions
H. Taheri, R. Pedarsani, and C. Thrampoulidis · 2021
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From data to decisions: Distributionally robust optimization is optimal
B. P. Van Parys, P. M. Esfahani, and D. Kuhn · 2021
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Fundamental barriers to high-dimensional regression with convex penalties
M. Celentano and A. Montanari · 2022
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Surprises in high-dimensional ridgeless least squares interpolation
T. Hastie, A. Montanari, S. Rosset, and R. J. Tibshirani · 2022
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The generalization error of random features regression: Precise asymptotics and the double descent curve
S. Mei and A. Montanari · 2022
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Universality of empirical risk minimization
A. Montanari and B. Saeed · 2022
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Universality of regularized regression estimators in high dimensions
Q. Han and Y. Shen · 2023
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S. Shafieezadeh-Abadeh, L. Aolaritei, F. Dörfler, and D. Kuhn · 2023
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