PAC-Bayesian Bounds based on the Rényi Divergence

Luc Bégin 1 Pascal Germain 2 François Laviolette 3 Jean-Francis Roy 3
2 SIERRA - Statistical Machine Learning and Parsimony
DI-ENS - Département d'informatique de l'École normale supérieure, CNRS - Centre National de la Recherche Scientifique, Inria de Paris
Abstract : We propose a simplified proof process for PAC-Bayesian generalization bounds, that allows to divide the proof in four successive inequalities, easing the "customization" of PAC-Bayesian theorems. We also propose a family of PAC-Bayesian bounds based on the Rényi divergence between the prior and posterior distributions, whereas most PAC-Bayesian bounds are based on the Kullback-Leibler divergence. Finally, we present an empirical evaluation of the tightness of each inequality of the simplified proof, for both the classical PAC-Bayesian bounds and those based on the Rényi divergence.
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Communication dans un congrès
International Conference on Artificial Intelligence and Statistics (AISTATS 2016), May 2016, Cadiz, Spain. 2016, Proceedings of the 19th International Conference on Artificial Intelligence and Statistics. 〈http://www.aistats.org/aistats2016/〉
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Soumis le : jeudi 20 octobre 2016 - 15:07:50
Dernière modification le : jeudi 26 avril 2018 - 10:28:58

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Luc Bégin, Pascal Germain, François Laviolette, Jean-Francis Roy. PAC-Bayesian Bounds based on the Rényi Divergence. International Conference on Artificial Intelligence and Statistics (AISTATS 2016), May 2016, Cadiz, Spain. 2016, Proceedings of the 19th International Conference on Artificial Intelligence and Statistics. 〈http://www.aistats.org/aistats2016/〉. 〈hal-01384783〉

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