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We derive generalization bounds for learning algorithms based on their robustness: the property that if a testing sample is "similar" to a training sample, then the testing error is close to the training error.
Stochastic Processes
J. L. Doob · 1953
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Theory of Pattern Recognition
V. N. Vapnik and A. Chervonenkis · 1974
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Robust Statistics
P. J. Huber · 1981
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Robust Regression and Outlier Detection
P. J. Rousseeuw and A. M. Leroy · 1987
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On the method of bounded differences
C. McDiarmid · 1989
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The necessary and sufficient conditions for consistency in the empirical risk minimization method
V. N. Vapnik and A. Chervonenkis · 1991
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Markov Chains and Stochastic Stability
S. P. Meyn and R. L. Tweedie · 1993
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Support vector networks
C. Cortes and V. N. Vapnik · 1995
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A Probabilistic Theory of Pattern Recognition
L. Devroye, L. Györfi, and G. Lugosi · 1996
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Regression shrinkage and selection via the Lasso
R. Tibshirani · 1996
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Scale-sensitive dimension, uniform convergence, and learnability
N. Alon, S. Ben-David, N. Cesa-Bianchi, and D. Haussler · 1997
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The sample complexity of pattern classification with neural networks: The size of the weight is more important than the size of the network
P. L. Bartlett · 1998
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Robust convex optimization
A. Ben-tal and A. Nemirovski · 1998
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Robust solutions of uncertain linear programs
A. Ben-Tal and A. Nemirovski · 1999
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Regularization networks and support vector machines
T. Evgeniou, M. Pontil, and T. Poggio · 2000
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Weak Convergence and Empirical Processes
A. W. van der Vaart and J. A. Wellner · 2000
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Learning with Kernels
B. Schölkopf and A. J. Smola · 2002
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The price of robustness
D. Bertsimas and M. Sim · 2004
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A second order cone programming formulation for classifying missing data
C. Bhattacharyya, K. S. Pannagadatta, and A. J. Smola · 2004
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General conditions for predictivity in learning theory
T. Poggio, R. Rifkin, S. Mukherjee, and P. Niyogi · 2004
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Local Rademacher complexities
P. L. Bartlett, O. Bousquet, and S. Mendelson · 2005
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Nightmare at test time: Robust learning by feature deletion
A. Globerson and S. Roweis · 2006
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Rademacher and Gaussian complexities: Risk bounds and structural results
P. L. Bartlett and S. Mendelson · 2002
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Stability and generalization
O. Bousquet and A. Elisseeff · 2002
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Hoeffding’s inequality for uniformly ergodic Markov chains
P. W. Glynn and D. Ormoneit · 2002
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Distribution-free inequalities for the deleted and holdout error estimates
L. Devroye and T. Wagner
Cited in the paper.
Distribution-free performance bounds for potential function rules
L. Devroye and T. Wagner
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Robust regression and Lasso
H. Xu, C. Caramanis, and S. Mannor
Cited in the paper.
Learning theory: Stability is sufficient for generalization and necessary and sufficient for consistency of empirical risk minimization
S. Mukherjee, P. Niyogi, T. Poggio, and R. Rifkin · 2006
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Second order cone programming approaches for handling missing and uncertain data
P. K. Shivaswamy, C. Bhattacharyya, and A. J. Smola · 2006
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Learnability and stability in the general learning setting
S. Shalev-Shwartz, O. Shamir, N. Srebro, and K. Sridharan · 2009
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