arXiv:1605.08636stat.ML
PAC-Bayesian Theory Meets Bayesian Inference
Early discovery. Linked by one identifiable commenter. This paper is outside the main ranking; a mention is not an endorsement.
Abstract
We exhibit a strong link between frequentist PAC-Bayesian risk bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization risk bounds maximizes the Bayesian marginal likelihood. This provides an alternative explanation to the Bayesian Occam's razor criteria, under the assumption that the data is generated by an i.i.d distribution. Moreover, as the negative log-likelihood is an unbounded loss function, we motivate and propose a PAC-Bayesian theorem tailored for the sub-gamma loss family, and we show that our approach is sound on classical Bayesian linear regression tasks.
Just to add on top of the quality reference provided by srean, I like to first drill in Bayesian principles and then use this article to derive PAC-Bayes from that: https://arxiv.org/abs/1605.08636 Regular PAC falls out by taking a uniform prior over a finite hypothesis class…
hodgehog11View on HNParent context