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We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds.
Beweis, daß jede menge wohlgeordnet werden kann
Ernst Zermelo · 1904
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On the uniform convergence of relative frequencies of events to their probabilities
V. N. Vapnik and A. Ya. Chervonenkis · 1971
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On the density of families of sets
N. Sauer · 1972
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A combinatorial problem; stability and order for models and theories in infinitary languages
Saharon Shelah · 1972
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Relating data compression and learnability
Nick Littlestone and Manfred K. Warmuth · 1986
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Some PAC-Bayesian theorems
D. McAllester · 1998
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Model selection and error estimation
Peter L. Bartlett, Stéphane Boucheron, and Gábor Lugosi · 2002
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PAC-Bayesian generalization error bounds for Gaussian process classification
M. Seeger · 2002
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PAC-Bayes & margins
John Langford and John Shawe-Taylor · 2003
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PAC-Bayesian stochastic model selection
D. McAllester · 2003
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PAC-Bayesian statistical learning theory
J.Y. Audibert · 2004
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A note on the PAC-Bayesian theorem
Andreas Maurer · 2004
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Optimal aggregation of classifiers in statistical learning
A.B. Tsybakov · 2004
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Tighter PAC-Bayes bounds
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Empirical minimization
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PAC-Bayesian Supervised Classification
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PAC-Bayes-empirical-Bernstein inequality
Ilya O. Tolstikhin and Yevgeny Seldin · 2013
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Fast rates in statistical and online learning
Tim van Erven, P. Grünwald, N. Mehta, M. Reid, and R. Williamson · 2015
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Exponential inequalities for martingales with applications
Xiequan Fan, Ion Grama, and Quansheng Liu · 2015
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A tight excess risk bound via a unified PAC-Bayesian-Rademacher-Shtarkov-MDL complexity
Peter D. Grünwald and Nishant A. Mehta · 2019
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PAC-Bayes un-expected Bernstein inequality
Zakaria Mhammedi, Peter Grünwald, and Benjamin Guedj · 2019
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Information-theoretic generalization bounds for SGLD via data-dependent estimates
Jeffrey Negrea, Mahdi Haghifam, Gintare Karolina Dziugaite, Ashish Khisti, and Daniel M Roy · 2019
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Fast-rate pac-bayes generalization bounds via shifted rademacher processes
Jun Yang, Shengyang Sun, and Daniel M Roy · 2019
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Non-vacuous generalization bounds at the ImageNet scale: a PAC-Bayesian compression approach
Wenda Zhou, Victor Veitch, Morgane Austern, Ryan P. Adams, and Peter Orbanz · 2019
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Approximate Bayesian inference
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Gintare Karolina Dziugaite and Daniel M Roy · 2017
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Information-theoretic analysis of generalization capability of learning algorithms
Aolin Xu and Maxim Raginsky · 2017
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Learners that use little information
Raef Bassily, Shay Moran, Ido Nachum, Jonathan Shafer, and Amir Yehudayoff · 2018
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A direct sum result for the information complexity of learning
Ido Nachum, Jonathan Shafer, and Amir Yehudayoff · 2018
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Pierre Alquier · 2020
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Fast rates for general unbounded loss functions: From ERM to generalized Bayes
Peter D. Grünwald and Nishant A. Mehta · 2020
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Mahdi Haghifam, Jeffrey Negrea, Ashish Khisti, Daniel M. Roy, and Gintare Karolina Dziugaite · 2020
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Generalization bounds via information density and conditional information density
Fredrik Hellström and Giuseppe Durisi · 2020
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A limitation of the PAC-Bayes framework
Roi Livni and Shay Moran · 2020
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Reasoning About Generalization via Conditional Mutual Information
Thomas Steinke and Lydia Zakynthinou · 2020
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On the role of data in pac-bayes
Gintare Karolina Dziugaite, Kyle Hsu, Waseem Gharbieh, Gabriel Arpino, and Daniel Roy · 2021
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