Definition: In this task, you are given a part of an article. Your task is to generate headline (title) for this text. Preferred headlines are under fifteen words.
Input: We exhibit a strong link between frequentist PAC-Bayesian bounds and the Bayesian marginal likelihood. That is, for the negative log-likelihood loss function, we show that the minimization of PAC-Bayesian generalization 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 a 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.

PAC-Bayesian Theory Meets Bayesian Inference