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- W2947545410 abstract "We present a new PAC-Bayesian generalization bound. Standard bounds contain a $sqrt{L_n cdot KL/n}$ complexity term which dominates unless $L_n$, the empirical error of the learning algorithm's randomized predictions, vanishes. We manage to replace $L_n$ by a term which vanishes in many more situations, essentially whenever the employed learning algorithm is sufficiently stable on the dataset at hand. Our new bound consistently beats state-of-the-art bounds both on a toy example and on UCI datasets (with large enough $n$). Theoretically, unlike existing bounds, our new bound can be expected to converge to $0$ faster whenever a Bernstein/Tsybakov condition holds, thus connecting PAC-Bayesian generalization and {em excess risk/} bounds---for the latter it has long been known that faster convergence can be obtained under Bernstein conditions. Our main technical tool is a new concentration inequality which is like Bernstein's but with $X^2$ taken outside its expectation." @default.
- W2947545410 created "2019-06-07" @default.
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- W2947545410 date "2019-12-09" @default.
- W2947545410 modified "2023-10-16" @default.
- W2947545410 title "PAC-Bayes Un-Expected Bernstein Inequality" @default.
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