# Fast-rate PAC-Bayes Generalization Bounds via Shifted Rademacher Processes

arXiv: https://arxiv.org/abs/1908.07585 · HTML: https://mlsanity.com/paper/1908.07585/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Aug 2019.

## Built on by (most cited first, 20 of 20)

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## Abstract (arXiv)

The developments of Rademacher complexity and PAC-Bayesian theory have been largely independent. One exception is the PAC-Bayes theorem of Kakade, Sridharan, and Tewari (2008), which is established via Rademacher complexity theory by viewing Gibbs classifiers as linear operators. The goal of this paper is to extend this bridge between Rademacher complexity and state-of-the-art PAC-Bayesian theory. We first demonstrate that one can match the fast rate of Catoni's PAC-Bayes bounds (Catoni, 2007) using shifted Rademacher processes (Wegkamp, 2003; Lecu'e and Mitchell, 2012; Zhivotovskiy and Hanneke, 2018). We then derive a new fast-rate PAC-Bayes bound in terms of the "flatness" of the empirical risk surface on which the posterior concentrates. Our analysis establishes a new framework for deriving fast-rate PAC-Bayes bounds and yields new insights on PAC-Bayesian theory.