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Bounding the generalization error of learning algorithms has a long history, which yet falls short in explaining various generalization successes including those of deep learning.
The sizes of compact subsets of Hilbert space and continuity of Gaussian processes
R. M. Dudley · 1967
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Evaluations de processus Gaussiens composes
X. Fernique · 1976
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Relating data compression and learnability
N. Littlestone and M. Warmuth · 1986
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Some PAC-Bayesian theorems
D. A. McAllester · 1999
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Stability and generalization
O. Bousquet and A. Elisseeff · 2002
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Introduction to statistical learning theory
O. Bousquet, S. Boucheron, and G. Lugosi · 2004
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PAC-Bayesian generic chaining
J. Audibert and O. Bousquet · 2004
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Local Rademacher complexities
P. L. Bartlett, O. Bousquet, and S. Mendelson · 2005
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Combining PAC-Bayesian and generic chaining bounds
J. Audibert and O. Bousquet · 2007
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Elements of Information Theory
T. M. Cover and J. A. Thomas · 2012
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Concentration Inequalities: A Nonasymptotic Theory of Independence
S. Boucheron, G. Lugosi, and P. Massart · 2013
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Understanding Machine Learning: From Theory to Algorithms
S. Shalev-Shwartz and S. Ben-David · 2014
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Upper and Lower Bounds for Stochastic Processes: Modern Methods and Classical Problems
M. Talagrand · 2014
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How much does your data exploration overfit? controlling bias via information usage
Generalization in deep learning
K. Kawaguchi, L. P. Kaelbling and Y. Bengio · 2017
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Dependence measures bounding the exploration bias for general measurements
J. Jiao, Y. Han and T. Weissman · 2017
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Generalizations of maximal inequalities to arbitrary selection rules
J. Jiao, Y. Han and T. Weissman · 2017
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Information-theoretic analysis of generalization capability of learning algorithms
A. Xu and M. Raginsky · 2017
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Learners that leak little information
R. Bassily, S. Moran, I. Nachum, J. Shafer and A. Yehudayoff · 2017
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D. Russo and J. Zou · 2015
Cited alongside, same era.
Probability in high dimension
R. van Handel · 2016
Cited alongside, same era.
Understanding deep learning requires rethinking generalization
C. Zhang, S. Bengio, M. Hardt, B. Recht and O. Vinyals · 2017
Cited alongside, same era.
To understand deep learning we need to understand kernel learning
M. Belkin, S. Ma, and S. Mandal · 2018
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High-Dimensional Probability: An Introduction with Applications in Data Science
R. Vershynin · 2018
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Generalization error bounds for noisy, iterative algorithms
A. Pensia, V. Jog and P. Loh · 2018
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