PAC-Bayes Bounds for Gibbs Posteriors via Singular Learning Theory
We derive explicit non-asymptotic PAC-Bayes generalization bounds for Gibbs posteriors, that is, data-dependent distributions over model parameters obtained by exponentially tilting a prior with the empirical risk. Unlike classical worst-case complexity bounds based on uniform laws of large numbers, which require explicit control of the model space in terms of metric entropy (integrals), our analysis yields posterior-averaged risk bounds that can be applied to overparameterized models and adapt to the data structure and the intrinsic model complexity. The bound involves a marginal-type integral over the parameter space, which we analyze using tools from singular learning theory to obtain ...
| Authors | Chenyang Wang, Yun Yang |
|---|---|
| Primary category | stat.ML |
| Published | 19 April 2026 |
| Last updated at source | 19 April 2026 |
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