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- W3174537209 abstract "We give a novel, unified derivation of conditional PAC-Bayesian and mutual information (MI) generalization bounds. We derive conditional MI bounds as an instance, with special choice of prior, of conditional MAC-Bayesian (Mean Approximately Correct) bounds, itself derived from conditional PAC-Bayesian bounds, where `conditional' means that one can use priors conditioned on a joint training and ghost sample. This allows us to get nontrivial PAC-Bayes and MI-style bounds for general VC classes, something recently shown to be impossible with standard PAC-Bayesian/MI bounds. Second, it allows us to get fast rates of order $O((text{KL}/n)^{gamma}$ for $gamma > 1/2$ if a Bernstein condition holds and for exp-concave losses (with $gamma=1$), which is impossible with both standard PAC-Bayes generalization and MI bounds. Our work extends the recent work by Steinke and Zakynthinou (2020) who handle MI with VC but neither PAC-Bayes nor fast rates and Mhammedi et al. (2019) who initiated fast rate PAC-Bayes generalization error bounds but handle neither MI nor general VC classes." @default.
- W3174537209 created "2021-07-05" @default.
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- W3174537209 date "2021-07-07" @default.
- W3174537209 modified "2023-09-26" @default.
- W3174537209 title "PAC-Bayes, MAC-Bayes and Conditional Mutual Information: Fast rate bounds that handle general VC classes" @default.
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