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We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood.
Ockham’s razor and Bayesian analysis
William H. Jeffreys and James O. Berger · 1992
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Bayesian interpolation
David J. C. MacKay · 1992
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A decision-theoretic generalization of on-line learning and an application to boosting
Yoav Freund and Robert E Schapire · 1997
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A PAC analysis of a Bayesian estimator
John Shawe-Taylor and Robert C. Williamson · 1997
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Some PAC-Bayesian theorems
David McAllester · 1999
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Bounds for averaging classifiers
John Langford and Matthias Seeger · 2001
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On discriminative vs. generative classifiers: A comparison of logistic regression and naive Bayes
Andrew Y. Ng and Michael I. Jordan · 2001
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PAC-Bayes & margins
John Langford and John Shawe-Taylor · 2002
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PAC-Bayesian generalization bounds for Gaussian processes
Matthias Seeger · 2002
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PAC-Bayesian stochastic model selection
David McAllester · 2003
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Generalization error bounds for Bayesian mixture algorithms
Ron Meir and Tong Zhang · 2003
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Bayesian Gaussian Process Models: PAC-Bayesian Generalisation Error Bounds and Sparse Approximations
Matthias Seeger · 2003
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Online bounds for Bayesian algorithms
Sham M. Kakade and Andrew Y. Ng · 2004
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A note on the PAC-Bayesian theorem
Andreas Maurer · 2004
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Tighter PAC-Bayes bounds
Amiran Ambroladze, Emilio Parrado-Hernández, and John Shawe-Taylor · 2006
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On Bayesian bounds
Arindam Banerjee · 2006
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Pattern Recognition and Machine Learning (Information Science and Statistics)
Christopher M. Bishop · 2006
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Gaussian Processes for Machine Learning
Carl Rasmussen and Chris Williams · 2006
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Information-theoretic upper and lower bounds for statistical estimation
Tong Zhang · 2006
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PAC-Bayesian supervised classification: the thermodynamics of statistical learning , volume 56
Olivier Catoni · 2007
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Suboptimal behavior of Bayes and MDL in classification under misspecification
Peter Grünwald and John Langford · 2007
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The Minimum Description Length Principle
Peter D. Grünwald · 2007
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Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity
Arnak S. Dalalyan and Alexandre B. Tsybakov · 2008
Learning efficient random maximum a-posteriori predictors with non-decomposable loss functions
Tamir Hazan, Subhransu Maji, Joseph Keshet, and Tommi S. Jaakkola · 2013
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Tighter PAC-Bayes bounds through distribution-dependent priors
Guy Lever, François Laviolette, and John Shawe-Taylor · 2013
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PAC-Bayes-empirical-Bernstein inequality
Ilya O. Tolstikhin and Yevgeny Seldin · 2013
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PAC-Bayesian theory for transductive learning
Luc Bégin, Pascal Germain, François Laviolette, and Jean-Francis Roy · 2014
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Inconsistency of Bayesian Inference for Misspecified Linear Models, and a Proposal for Repairing It
Peter Grünwald and Thijs van Ommen · 2014
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Robust forward algorithms via PAC-Bayes and Laplace distributions
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PAC-Bayesian learning of linear classifiers
Pascal Germain, Alexandre Lacasse, François Laviolette, and Mario Marchand · 2009
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Model selection: Beyond the Bayesian/frequentist divide
Isabelle Guyon, Amir Saffari, Gideon Dror, and Gavin C. Cawley · 2010
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PAC-Bayesian analysis of co-clustering and beyond
Yevgeny Seldin and Naftali Tishby · 2010
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Approximate inference for the loss-calibrated Bayesian
Simon Lacoste-Julien, Ferenc Huszar, and Zoubin Ghahramani · 2011
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Generalization bounds and consistency for latent structural probit and ramp loss
David McAllester and Joseph Keshet · 2011
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PAC-Bayesian analysis of contextual bandits
Yevgeny Seldin, Peter Auer, François Laviolette, John Shawe-Taylor, and Ronald Ortner · 2011
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Asf Noy and Koby Crammer · 2014
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A PAC-Bayesian bound for lifelong learning
Anastasia Pentina and Christoph H. Lampert · 2014
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Risk bounds for the majority vote: From a PAC-Bayesian analysis to a learning algorithm
Pascal Germain, Alexandre Lacasse, Francois Laviolette, Mario Marchand, and Jean-Francis Roy · 2015
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Probabilistic machine learning and artificial intelligence
Zoubin Ghahramani · 2015
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Agnostic Bayes
Alexandre Lacoste · 2015
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On the properties of variational approximations of Gibbs posteriors
Pierre Alquier, James Ridgway, and Nicolas Chopin · 2016
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PAC-Bayesian bounds based on the Rényi divergence
Luc Bégin, Pascal Germain, François Laviolette, and Jean-Francis Roy · 2016
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A general framework for updating belief distributions
P. G. Bissiri, C. C. Holmes, and S. G. Walker · 2016
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A new PAC-Bayesian perspective on domain adaptation
Pascal Germain, Amaury Habrard, François Laviolette, and Emilie Morvant · 2016
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Fast rates with unbounded losses
Peter D. Grünwald and Nishant A. Mehta · 2016
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On the frequentist properties of Bayesian nonparametric methods
Judith Rousseau · 2016
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