PAC-Bayesian Theory Meets Bayesian Inference
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.
Cite
@article{arxiv.1605.08636,
title = {PAC-Bayesian Theory Meets Bayesian Inference},
author = {Pascal Germain and Francis Bach and Alexandre Lacoste and Simon Lacoste-Julien},
journal= {arXiv preprint arXiv:1605.08636},
year = {2017}
}
Comments
Published at NIPS 2015 (http://papers.nips.cc/paper/6569-pac-bayesian-theory-meets-bayesian-inference)