We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.
MiS Preprint
21/2021
PAC-Bayes and Information Complexity
Pradeep Kumar Banerjee and Guido Montúfar
Abstract
We point out that a number of well-known PAC-Bayesian-style and information-theoretic generalization bounds for randomized learning algorithms can be derived under a common framework starting from a fundamental information exponential inequality. We also obtain new bounds for data-dependent priors and unbounded loss functions. Optimizing these bounds naturally gives rise to a method called Information Complexity Minimization for which we discuss two practical examples for learning with neural networks, namely Entropy- and PAC-Bayes- SGD.
